y2+y=51

Solution for y2+y=51 equation:

y2+y=51

We move all terms to the left:

y2+y-(51)=0

We add all the numbers together, and all the variables

y^2+y-51=0

a = 1; b = 1; c = -51;
Δ = b2-4ac
Δ = 12-4·1·(-51)
Δ = 205
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{205}}{2*1}=\frac{-1-\sqrt{205}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{205}}{2*1}=\frac{-1+\sqrt{205}}{2}
$