x^2-30x=112.5

Solution for x^2-30x=112.5 equation:

x^2-30x=112.5

We move all terms to the left:

x^2-30x-(112.5)=0

We add all the numbers together, and all the variables

x^2-30x-112.5=0

a = 1; b = -30; c = -112.5;
Δ = b2-4ac
Δ = -302-4·1·(-112.5)
Δ = 1350
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:

$\sqrt{\Delta}=\sqrt{1350}=\sqrt{225*6}=\sqrt{225}*\sqrt{6}=15\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-15\sqrt{6}}{2*1}=\frac{30-15\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+15\sqrt{6}}{2*1}=\frac{30+15\sqrt{6}}{2}
$