31x^2+125x-150=0

Solution for 31x^2+125x-150=0 equation:

31x^2+125x-150=0

a = 31; b = 125; c = -150;
Δ = b2-4ac
Δ = 1252-4·31·(-150)
Δ = 34225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34225}=185$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-185}{2*31}=\frac{-310}{62}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+185}{2*31}=\frac{60}{62}
=30/31
$