5x^2-8x-25=0

Solution for 5x^2-8x-25=0 equation:

5x^2-8x-25=0

a = 5; b = -8; c = -25;
Δ = b2-4ac
Δ = -82-4·5·(-25)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{141}}{2*5}=\frac{8-2\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{141}}{2*5}=\frac{8+2\sqrt{141}}{10}
$