0=150x-x^2-150

Solution for 0=150x-x^2-150 equation:

0=150x-x^2-150

We move all terms to the left:

0-(150x-x^2-150)=0

We add all the numbers together, and all the variables

-(150x-x^2-150)=0

We get rid of parentheses

x^2-150x+150=0

a = 1; b = -150; c = +150;
Δ = b2-4ac
Δ = -1502-4·1·150
Δ = 21900
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:

$\sqrt{\Delta}=\sqrt{21900}=\sqrt{100*219}=\sqrt{100}*\sqrt{219}=10\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{219}}{2*1}=\frac{150-10\sqrt{219}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{219}}{2*1}=\frac{150+10\sqrt{219}}{2}
$