x^2-17x=-52

Solution for x^2-17x=-52 equation:

x^2-17x=-52

We move all terms to the left:

x^2-17x-(-52)=0

We add all the numbers together, and all the variables

x^2-17x+52=0

a = 1; b = -17; c = +52;
Δ = b2-4ac
Δ = -172-4·1·52
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-9}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+9}{2*1}=\frac{26}{2}
=13
$