25x^2+172x-8=0

Solution for 25x^2+172x-8=0 equation:

25x^2+172x-8=0

a = 25; b = 172; c = -8;
Δ = b2-4ac
Δ = 1722-4·25·(-8)
Δ = 30384
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:

$\sqrt{\Delta}=\sqrt{30384}=\sqrt{144*211}=\sqrt{144}*\sqrt{211}=12\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172)-12\sqrt{211}}{2*25}=\frac{-172-12\sqrt{211}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172)+12\sqrt{211}}{2*25}=\frac{-172+12\sqrt{211}}{50}
$