Solve 6x² + 3x – 18 = 0 using the quadratic formula. ?

6x^2 + 3x - 18 = 0
(6x^2 + 3x - 18)/3 = 0/3
2x^2 + x - 6 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 2
b = 1
c = -6

x = [-1 ±√(1 + 48)]/4
x = [-1 ±√49]/4
x = [-1 ±7]/4

x = [-1 + 7]/4
x = 6/4
x = 3/2 (1.5)

x = [-1 - 7]/4
x = -8/4
x = -2

∴ x = -2 , 3/2 (1.5)

ingredient. ingredient rule: a²+2ab+b²=(a+b)² 2 3 3 6 (2x-3)(3x+6)=0 so... x=3/2,-6/3 simplifed. x=3/2,-2 playstation . i'm good considering the fact which you are able to blug in the numbers i've got given you and it will constantly = 0 relative to the given numbers. it particularly is predicated on the rule of thumb.

2x² + x - 6 = 0
x = [ - 1 ± √ (1 + 48 ) ] / 4
x = [ - 1 ± √ (49) ] / 4
x = [ - 1 ± 7 ] / 4
x = 6/4 , x = - 2
x = 3/2 , x = - 2

firstly, u can plot it into a graph.
secondly, do it algebraically.

here is the way to solve it algebraically:
6x² + 3x – 18 = 0
factorise it:
3(2x² + x – 9) = 0

(2x² + x – 9) = 0
factors of -6 (coefficient of c)
1, -6
2, -3
-1, 6
-2, 3
factors of 2 (coefficient of x²)
1, 2
thus, we have to find either
(1*1)+(-6*2)
OR
(1*2)+(-6*1)
OR
(-1*1)+(6*2)
OR
(-1*2)+(6*1)
OR
(-2*2)+(3*1)
OR
(3*2)+(-2*1)
OR
(2*2)+(-3*1)
OR
(-3*2)+(2*1)

(rmb that factor of 2 on the right)
(factor of -6 on the left)

= coefficient of x.
thus, (2*2)+(-3*1) = 1
therefore
(x + 2)(2x - 3) = 0

x = -2 OR 3

the quadratic formula is:

-b ± SQRT(b2 - 4ac)
x = -----------------------------
2a

the general formula of a quadratic equation is:

ax2 + bx + c = 0, which is equivalet to 6x² + 3x – 18 = 0

where,

a= 6, b=3, c=-18

Using the formula:

-b ± SQRT(b2 - 4ac)
x = ------------------------------
2a

we substitute the value in, which gives us:

-3 ± SQRT((3)2 - 4(6)(-18)
x = -------------------------------------
2(6)

-3 ± SQRT(9 +432)
x = -----------------------------
12

-3 ± SQRT(441)
x = ------------------------
12

-3 ± 21
x = --------------
12

-3+21 -3-21
x = ----------- or ------------
12 12

x = 1.5 or -4

i hope this helps :)

Instead of using the formula, I would divide it by 6 and come down to x^2 + 0.5x - 3 = 0

Then split the equation as x^2 +2x -1.5x -3=0

Then x(x+2) -1.5(x+2) = 0

Therefore (x-1.5) (x+2) = 0

so, x = 1.5 or x = -2

All the best

you don't have to use formula at all

First factor out 3, so you eqation will be
2x^2+x-6=0
(2x-3)(x+2)=0
x=3/2 or x=-2

The quadratic formula is x = (-b±√(b^2-4ac))/2a
where the general quadratic equation is y=ax^2 +bx + c.
So to solve your equation you need to sub b=3 a-6 and c=-18 into the quadratic formula.
x = (-3±√(3^2-4(6)(-18)))/(2(6))
x = (-3±√441)/12
x = (-3+√441)/12 = 1.5 and x = (-3-√441)/12 = -2

Negative B plus or minus the square root of B squared minus 4AC all over 2A, where the formula is AX^2 + BX + C. Just plug in the values. Look at this place for extra help:
http://www.purplemath.com/modules/quadform.htm

x = (-3 + sqrt(3^2 - 4 * 6 * 18)) / (2 * 6) = -0.25 + 1.71391365 i
x = (-3 + sqrt(3^2 - 4 * 6 * 18)) / (2 * 6) = -0.25 - 1.71391365 i

the above are the values of x

see the source link for explanation