(-3x+6)=(6x^2-5x+5)

Solution for (-3x+6)=(6x^2-5x+5) equation:

(-3x+6)=(6x^2-5x+5)

We move all terms to the left:

(-3x+6)-((6x^2-5x+5))=0

We get rid of parentheses

-3x-((6x^2-5x+5))+6=0


We calculate terms in parentheses: -((6x^2-5x+5)), so:

(6x^2-5x+5)

We get rid of parentheses

6x^2-5x+5

Back to the equation:

-(6x^2-5x+5)


We get rid of parentheses

-6x^2-3x+5x-5+6=0

We add all the numbers together, and all the variables

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

a = -6; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-6)·1
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-6}=\frac{-2-2\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-6}=\frac{-2+2\sqrt{7}}{-12}
$