3(y-5)y=8

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

3(y-5)y=8

We move all terms to the left:

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

We multiply parentheses

3y^2-15y-8=0

a = 3; b = -15; c = -8;
Δ = b2-4ac
Δ = -152-4·3·(-8)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{321}}{2*3}=\frac{15-\sqrt{321}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{321}}{2*3}=\frac{15+\sqrt{321}}{6}
$