u^2-13u=36

Solution for u^2-13u=36 equation:

u^2-13u=36

We move all terms to the left:

u^2-13u-(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:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{313}}{2*1}=\frac{13-\sqrt{313}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*1}=\frac{13+\sqrt{313}}{2}
$