X^2-7x+12=4x-4

Solution for X^2-7x+12=4x-4 equation:

X^2-7X+12=4X-4

We move all terms to the left:

X^2-7X+12-(4X-4)=0

We get rid of parentheses

X^2-7X-4X+4+12=0

We add all the numbers together, and all the variables

X^2-11X+16=0

a = 1; b = -11; c = +16;
Δ = b2-4ac
Δ = -112-4·1·16
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{57}}{2*1}=\frac{11-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{57}}{2*1}=\frac{11+\sqrt{57}}{2}
$