6x^2-11x+6=-4x+4

Solution for 6x^2-11x+6=-4x+4 equation:

6x^2-11x+6=-4x+4

We move all terms to the left:

6x^2-11x+6-(-4x+4)=0

We get rid of parentheses

6x^2-11x+4x-4+6=0

We add all the numbers together, and all the variables

6x^2-7x+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$