(5x^2)-8x-125=0

Solution for (5x^2)-8x-125=0 equation:

(5x^2)-8x-125=0

a = 5; b = -8; c = -125;
Δ = b2-4ac
Δ = -82-4·5·(-125)
Δ = 2564
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:

$\sqrt{\Delta}=\sqrt{2564}=\sqrt{4*641}=\sqrt{4}*\sqrt{641}=2\sqrt{641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{641}}{2*5}=\frac{8-2\sqrt{641}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{641}}{2*5}=\frac{8+2\sqrt{641}}{10}
$