51y-y^2-518=0

Solution for 51y-y^2-518=0 equation:

51y-y^2-518=0

We add all the numbers together, and all the variables

-1y^2+51y-518=0

a = -1; b = 51; c = -518;
Δ = b2-4ac
Δ = 512-4·(-1)·(-518)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-23}{2*-1}=\frac{-74}{-2}
=+37
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+23}{2*-1}=\frac{-28}{-2}
=+14
$