5x^2-5x-75=75

Solution for 5x^2-5x-75=75 equation:

5x^2-5x-75=75

We move all terms to the left:

5x^2-5x-75-(75)=0

We add all the numbers together, and all the variables

5x^2-5x-150=0

a = 5; b = -5; c = -150;
Δ = b2-4ac
Δ = -52-4·5·(-150)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-55}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+55}{2*5}=\frac{60}{10}
=6
$