solve the quadratic equation...can't figure out?

The quadratic formula is:

x = [ -b ± √(b² - 4ac)] / 2a

when you have:

ax² + bx + c = 0

So first, set your equation to fit the form, then you can plug in a, b, and c values to solve for x:

4x² = -12x - 3
4x² + 12x + 3 = 0

a = 4
b = 12
c = 3

So we have:

x = [ -b ± √(b² - 4ac)] / 2a
x = [ -12 ± √(12² - 4(4)(3))] / 2(4)
x = [ -12 ± √(144 - 48)] / 8
x = [ -12 ± √(96)] / 8
x = [ -12 ± √(16 * 6)] / 8
x = [ -12 ± 4√(6)] / 8
x = ( -3 ± √6 ) / 2

4x^2 = -12x - 3
4x^2 + 12x + 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 4
b = 12
c = 3

x = [-12 ±√(144 - 48)]/8
x = [-12 ±√96]/8
x = [-12 ±√(4^2 * 6)]/8
x = [-12 ±4√6]/8
x = [-3 ±√6]/2

∴ x = [-3 ±√6]/2

4x^2 +12x +3=0
x= (-12+or-rootof(144-48))/8
= (-12+or-rootof(96))/8
= (-12+or-9.797)/8
=(-12+9.797)/8 or (-12-9.797)/8
= -2.203/8 or - 21.797/8
= -0.275 or -2.724
= -0.28 or -2.72
x={ -0.28, -2.72} (correct to two decimal places)

The quadratic equation must be in the format of:
ax^2 + bx + c = 0

So we must get everything on one side.

4x^2 = -12x - 3
+12x + 3 +12x + 3
4x^2 + 12x + 3 = 0

We get one side to the other by performing the inverse operation (instead of being -12x and -3 we do +3 and +12x to both sides).

Now, the quadratic equation is:

x = -b ± √( b^2 - (4ac))
-----------------------------
2a

Plug in:

x = -12 ± √ 96
--------------------------------
8

In most instances it is just as well to leave the squareroot symbol instead of solving with decimal. Thus, you can either do

-12 ± 9.79795897
-------------------------------
8

or just leave it as -12 +- √ 96.

Thus, your answers are:

-12 + √ 96
-----------------
8
or

-12 - √ 96
-----------------
8

Or the more literal answer would be:

x = -0.275255129
or
x = -2.72474487.

To make sure we are correct, we should then plug these figures into the original equation to make sure we are correct.

4x^2 = - 12x - 3
move it all to one side
4x^2 + 12x + 3 = 0
you have two equations one is
[-12+sqrt(12^2 - 4*4*3)]/2*4
[-12+sqrt(96)]/8
[-12+4sqrt(6)]/8
-3/2 + (1/2)*sqrt(6)

the other is
[-12-sqrt(12^2 - 4*4*3)]/2*4
[-12-sqrt(96)]/8
[-12-4sqrt(6)]/8
-3/2 - (1/2)*sqrt(6)