x^2-30x-150=-75

Solution for x^2-30x-150=-75 equation:

x^2-30x-150=-75

We move all terms to the left:

x^2-30x-150-(-75)=0

We add all the numbers together, and all the variables

x^2-30x-75=0

a = 1; b = -30; c = -75;
Δ = b2-4ac
Δ = -302-4·1·(-75)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-20\sqrt{3}}{2*1}=\frac{30-20\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+20\sqrt{3}}{2*1}=\frac{30+20\sqrt{3}}{2}
$