(3y-5)y=212

Solution for (3y-5)y=212 equation:

(3y-5)y=212

We move all terms to the left:

(3y-5)y-(212)=0

We multiply parentheses

3y^2-5y-212=0

a = 3; b = -5; c = -212;
Δ = b2-4ac
Δ = -52-4·3·(-212)
Δ = 2569
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{-(-5)-\sqrt{2569}}{2*3}=\frac{5-\sqrt{2569}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2569}}{2*3}=\frac{5+\sqrt{2569}}{6}
$