5y^2-28y-100=0

Solution for 5y^2-28y-100=0 equation:

5y^2-28y-100=0

a = 5; b = -28; c = -100;
Δ = b2-4ac
Δ = -282-4·5·(-100)
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{174}}{2*5}=\frac{28-4\sqrt{174}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{174}}{2*5}=\frac{28+4\sqrt{174}}{10}
$