5y(3y-4)=8

Solution for 5y(3y-4)=8 equation:

5y(3y-4)=8

We move all terms to the left:

5y(3y-4)-(8)=0

We multiply parentheses

15y^2-20y-8=0

a = 15; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·15·(-8)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{55}}{2*15}=\frac{20-4\sqrt{55}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{55}}{2*15}=\frac{20+4\sqrt{55}}{30}
$