x(x+15)=65

Solution for x(x+15)=65 equation:

x(x+15)=65

We move all terms to the left:

x(x+15)-(65)=0

We multiply parentheses

x^2+15x-65=0

a = 1; b = 15; c = -65;
Δ = b2-4ac
Δ = 152-4·1·(-65)
Δ = 485
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{-(15)-\sqrt{485}}{2*1}=\frac{-15-\sqrt{485}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{485}}{2*1}=\frac{-15+\sqrt{485}}{2}
$