y^2+10y-72=0

Solution for y^2+10y-72=0 equation:

y^2+10y-72=0

a = 1; b = 10; c = -72;
Δ = b2-4ac
Δ = 102-4·1·(-72)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{97}}{2*1}=\frac{-10-2\sqrt{97}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{97}}{2*1}=\frac{-10+2\sqrt{97}}{2}
$