0=30x-x^2-100

Solution for 0=30x-x^2-100 equation:

0=30x-x^2-100

We move all terms to the left:

0-(30x-x^2-100)=0

We add all the numbers together, and all the variables

-(30x-x^2-100)=0

We get rid of parentheses

x^2-30x+100=0

a = 1; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·1·100
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{5}}{2*1}=\frac{30-10\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{5}}{2*1}=\frac{30+10\sqrt{5}}{2}
$