4x^2-20x=75

Solution for 4x^2-20x=75 equation:

4x^2-20x=75

We move all terms to the left:

4x^2-20x-(75)=0

a = 4; b = -20; c = -75;
Δ = b2-4ac
Δ = -202-4·4·(-75)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40}{2*4}=\frac{60}{8}
=7+1/2
$