x(x+30)=60

Solution for x(x+30)=60 equation:

x(x+30)=60

We move all terms to the left:

x(x+30)-(60)=0

We multiply parentheses

x^2+30x-60=0

a = 1; b = 30; c = -60;
Δ = b2-4ac
Δ = 302-4·1·(-60)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{285}}{2*1}=\frac{-30-2\sqrt{285}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{285}}{2*1}=\frac{-30+2\sqrt{285}}{2}
$