x^2-7x+4=2x-8

Solution for x^2-7x+4=2x-8 equation:

x^2-7x+4=2x-8

We move all terms to the left:

x^2-7x+4-(2x-8)=0

We get rid of parentheses

x^2-7x-2x+8+4=0

We add all the numbers together, and all the variables

x^2-9x+12=0

a = 1; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·1·12
Δ = 33
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{-(-9)-\sqrt{33}}{2*1}=\frac{9-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*1}=\frac{9+\sqrt{33}}{2}
$