0=x^2-30x-112.5

Solution for 0=x^2-30x-112.5 equation:

0=x^2-30x-112.5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+30x+112.5=0

We add all the numbers together, and all the variables

-1x^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}
$