6y^2-y-51=0

Solution for 6y^2-y-51=0 equation:

6y^2-y-51=0

We add all the numbers together, and all the variables

6y^2-1y-51=0

a = 6; b = -1; c = -51;
Δ = b2-4ac
Δ = -12-4·6·(-51)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*6}=\frac{-34}{12}
=-2+5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*6}=\frac{36}{12}
=3
$