15y^2-31y-24=0

Solution for 15y^2-31y-24=0 equation:

15y^2-31y-24=0

a = 15; b = -31; c = -24;
Δ = b2-4ac
Δ = -312-4·15·(-24)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-49}{2*15}=\frac{-18}{30}
=-3/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+49}{2*15}=\frac{80}{30}
=2+2/3
$