What is −6x + 2 = −3x^2?

3x^2 - 6x + 2 = 0

If ax^2+bx+c = 0, then by the quadratic formula

x = (-b +/- sqrt(b^2 - 4ac))/2a

Applying the formula gives

x = (6 +/- sqrt(36 - 4(3)(2))) / 6

x = (6 +/- sqrt(12))/6

Which can be simplified to:

x = 1+1/(sqrt(3)) or x = 1 - 1/(sqrt(3))

===> 3x^2 --6x +2 =0
So x = +6/6 +/-- sq rt(36-24) / 6
ie x = 1 +/-- (1/3) sqrt(3)
ie x = 1 + (1/3) * sqrt(3) and 1 -- (1/3) *sqrt(3)

-6x + 2 =-3x^2 (plus 3x^2)
3x^2 - 6x + 2=0 (factorize using quadratic equation)
x= (6+2√3)/6 or (6-2√3)/6
= (3+√3)/3 or (3-√3)/3

3x^2-6x+2=0

x1,2 = [-b + - V{b^-4ac} ] : 2a
= [ 6 +- V{36-4(3)(2)}] : 2(3)
= [6 +- V12 ] : 6
= [6 +- 2V3 ] : 6
= 1 +- 1/3 V3
x1 = 1 + 1/3 V3
x2 = 1 - 1/3V3

The simple answer is that it is an equation.

Wording should be " Solve the following equation" :-

- 6x + 2 = - 3 x ²

3 x ² - 6x + 2 = 0

x = [ - b ± √ ( b ² - 4 a c ) ] / 2 a

x = [ 6 ± √ ( 36 - 24 ) ] / 6

x = [ 6 ± √ ( 12 ) ] / 6

x = [ 6 ± 2√3 ] / 6

x = 1 ± √3/3

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

a = 3
b = -6
c = 2

x = [6 ± √(36 - 24)]/6
x = [6 ± √12]/6
x = [6 ± √(2^2 * 3)]/6
x = [6 ± 2√3]/6
x = [3 ± √3]/3

∴ x = [3 ± √3]/3