X^2+10x-52=3x-8

Solution for X^2+10x-52=3x-8 equation:

X^2+10X-52=3X-8

We move all terms to the left:

X^2+10X-52-(3X-8)=0

We get rid of parentheses

X^2+10X-3X+8-52=0

We add all the numbers together, and all the variables

X^2+7X-44=0

a = 1; b = 7; c = -44;
Δ = b2-4ac
Δ = 72-4·1·(-44)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*1}=\frac{8}{2}
=4
$