x^2=13x+36

Solution for x^2=13x+36 equation:

x^2=13x+36

We move all terms to the left:

x^2-(13x+36)=0

We get rid of parentheses

x^2-13x-36=0

a = 1; b = -13; c = -36;
Δ = b2-4ac
Δ = -132-4·1·(-36)
Δ = 313
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{-(-13)-\sqrt{313}}{2*1}=\frac{13-\sqrt{313}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*1}=\frac{13+\sqrt{313}}{2}
$