solve the equation using the quadratic equation formula.?

2x^2 - 6x + 2 = 0
x^2 - 3x + 1 = 0

Using quadratic formula:
x = [3 ± √(9 - 4)]/2
x = (3 ± √5)/5

2x^2 = 6x - 2
2x^2 - 6x + 2 = 0

x = [-b ±√(b^2 - 4ac)]/2a
a = 2
b = -6
c = 2
x = [6 ±√(36 - 16)]/4
x = [6 ±√20]/4
x = [6 ±4.47]/4 (approx.)

x = [6 + 4.47]/4
x = 10.47/4
x = 2.6175

x = [6 - 4.47]/4
x = 3.3825/4
x = 0.845625

∴ x = 2.6175 , 0.845625 (approx.)

ax^2+bx+c
2x^2=6x-2 rearrange 2x^2 -6x+2= 0

a=2
b=-6
c=2

x=(-b±√b^2-4ac)/2a
x=(6±√36-16)/4
x= (6±√20)/4

x1=(6+√20)/4= 2.618033989
x2=(6-√20)/4= 0.38196660113

let the roots of the equation 2x^2=6x-2 be x1 & x2,
then using the quadratic equation formula we have
x1, x2 = (6+/-sqrt(20))/2 and as such,
without any loss of generaliity,
x1 = (3+sqrt(5))/2 and x2= (3-sqrt(5))/2

2x^2 - 6x + 2 = 0
divide all terms by 2
x^2 - 3x + 1 = 0
a = 1 . . . b = -3 . . .c = 1
x = [ -(-3) +- sqrt((-3)^2 - 4(1)(1) )] / (2*1)
x = [3+- sqrt5] / 2
x = [3 + sqrt5] / 2 or x = [3 - sqrt5] / 2

Hope this helps!

I get for an answer [3±√5] / 2.
One answer is ≈2.618; other ≈.382.
- - - - - -
2x^2=6x-2 becomes

x² - 3x + 1 = 0 (after simplification).

Now plug into the quadratic formula
x = [-b ± √(b² - 4ac)] / (2a)

where a=1; b= -3; c=1

= 2x^2 - 6x + 2

Formula = (-b ± sqrt(b^2 - 4ac))/2a

a = 2
b = -6
c = 2

Work it out from there, first time using + where the ± sign is, second time using -.

x² - 3x + 2 = 0
(x - 2)(x - 1) = 0
x = 2 , x = 1
OR
x = [ 3 ± √ (9 - 8 ) ] / 2
x = [ 3 ± 1 ] / 2
x = 2 , x = 1