3y^2-y-36=0

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

3y^2-y-36=0

We add all the numbers together, and all the variables

3y^2-1y-36=0

a = 3; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·3·(-36)
Δ = 433
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{-(-1)-\sqrt{433}}{2*3}=\frac{1-\sqrt{433}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{433}}{2*3}=\frac{1+\sqrt{433}}{6}
$