18y^2-18y-5=51

Solution for 18y^2-18y-5=51 equation:

18y^2-18y-5=51

We move all terms to the left:

18y^2-18y-5-(51)=0

We add all the numbers together, and all the variables

18y^2-18y-56=0

a = 18; b = -18; c = -56;
Δ = b2-4ac
Δ = -182-4·18·(-56)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-66}{2*18}=\frac{-48}{36}
=-1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+66}{2*18}=\frac{84}{36}
=2+1/3
$