5x2-50x=75

Solution for 5x2-50x=75 equation:

5x^2-50x=75

We move all terms to the left:

5x^2-50x-(75)=0

a = 5; b = -50; c = -75;
Δ = b2-4ac
Δ = -502-4·5·(-75)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20\sqrt{10}}{2*5}=\frac{50-20\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20\sqrt{10}}{2*5}=\frac{50+20\sqrt{10}}{10}
$