-150+(-45x)+5x^2=0

Solution for -150+(-45x)+5x^2=0 equation:

-150+(-45x)+5x^2=0

We get rid of parentheses

5x^2-45x-150=0

a = 5; b = -45; c = -150;
Δ = b2-4ac
Δ = -452-4·5·(-150)
Δ = 5025
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:

$\sqrt{\Delta}=\sqrt{5025}=\sqrt{25*201}=\sqrt{25}*\sqrt{201}=5\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{201}}{2*5}=\frac{45-5\sqrt{201}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{201}}{2*5}=\frac{45+5\sqrt{201}}{10}
$