5y^2+26y-108=0

Solution for 5y^2+26y-108=0 equation:

5y^2+26y-108=0

a = 5; b = 26; c = -108;
Δ = b2-4ac
Δ = 262-4·5·(-108)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{709}}{2*5}=\frac{-26-2\sqrt{709}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{709}}{2*5}=\frac{-26+2\sqrt{709}}{10}
$