4y^2-24y-31=0

Solution for 4y^2-24y-31=0 equation:

4y^2-24y-31=0

a = 4; b = -24; c = -31;
Δ = b2-4ac
Δ = -242-4·4·(-31)
Δ = 1072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{67}}{2*4}=\frac{24-4\sqrt{67}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{67}}{2*4}=\frac{24+4\sqrt{67}}{8}
$