y^2-120y-238=0

Solution for y^2-120y-238=0 equation:

y^2-120y-238=0

a = 1; b = -120; c = -238;
Δ = b2-4ac
Δ = -1202-4·1·(-238)
Δ = 15352
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:

$\sqrt{\Delta}=\sqrt{15352}=\sqrt{4*3838}=\sqrt{4}*\sqrt{3838}=2\sqrt{3838}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3838}}{2*1}=\frac{120-2\sqrt{3838}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3838}}{2*1}=\frac{120+2\sqrt{3838}}{2}
$