125x^2-185x-8=0

Solution for 125x^2-185x-8=0 equation:

125x^2-185x-8=0

a = 125; b = -185; c = -8;
Δ = b2-4ac
Δ = -1852-4·125·(-8)
Δ = 38225
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:

$\sqrt{\Delta}=\sqrt{38225}=\sqrt{25*1529}=\sqrt{25}*\sqrt{1529}=5\sqrt{1529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-185)-5\sqrt{1529}}{2*125}=\frac{185-5\sqrt{1529}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185)+5\sqrt{1529}}{2*125}=\frac{185+5\sqrt{1529}}{250}
$