3y^2-24y-47=0

Solution for 3y^2-24y-47=0 equation:

3y^2-24y-47=0

a = 3; b = -24; c = -47;
Δ = b2-4ac
Δ = -242-4·3·(-47)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{285}}{2*3}=\frac{24-2\sqrt{285}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{285}}{2*3}=\frac{24+2\sqrt{285}}{6}
$