3y^2-y-51=0

Solution for 3y^2-y-51=0 equation:

3y^2-y-51=0

We add all the numbers together, and all the variables

3y^2-1y-51=0

a = 3; b = -1; c = -51;
Δ = b2-4ac
Δ = -12-4·3·(-51)
Δ = 613
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{613}}{2*3}=\frac{1-\sqrt{613}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{613}}{2*3}=\frac{1+\sqrt{613}}{6}
$