X^2-30x=60

Solution for X^2-30x=60 equation:

X^2-30X=60

We move all terms to the left:

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}
$