3y^2-31y+36=0

Solution for 3y^2-31y+36=0 equation:

3y^2-31y+36=0

a = 3; b = -31; c = +36;
Δ = b2-4ac
Δ = -312-4·3·36
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-23}{2*3}=\frac{8}{6}
=1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+23}{2*3}=\frac{54}{6}
=9
$