20x^2-75=0

Solution for 20x^2-75=0 equation:

20x^2-75=0

a = 20; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·20·(-75)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*20}=\frac{0-20\sqrt{15}}{40}
=-\frac{20\sqrt{15}}{40}
=-\frac{\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*20}=\frac{0+20\sqrt{15}}{40}
=\frac{20\sqrt{15}}{40}
=\frac{\sqrt{15}}{2}
$