125x^2-20x-90=0

Solution for 125x^2-20x-90=0 equation:

125x^2-20x-90=0

a = 125; b = -20; c = -90;
Δ = b2-4ac
Δ = -202-4·125·(-90)
Δ = 45400
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:

$\sqrt{\Delta}=\sqrt{45400}=\sqrt{100*454}=\sqrt{100}*\sqrt{454}=10\sqrt{454}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{454}}{2*125}=\frac{20-10\sqrt{454}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{454}}{2*125}=\frac{20+10\sqrt{454}}{250}
$