x^2-15x=36

Solution for x^2-15x=36 equation:

x^2-15x=36

We move all terms to the left:

x^2-15x-(36)=0

a = 1; b = -15; c = -36;
Δ = b2-4ac
Δ = -152-4·1·(-36)
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{41}}{2*1}=\frac{15-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{41}}{2*1}=\frac{15+3\sqrt{41}}{2}
$