y^2-36y-248=0

Solution for y^2-36y-248=0 equation:

y^2-36y-248=0

a = 1; b = -36; c = -248;
Δ = b2-4ac
Δ = -362-4·1·(-248)
Δ = 2288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{143}}{2*1}=\frac{36-4\sqrt{143}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{143}}{2*1}=\frac{36+4\sqrt{143}}{2}
$