5y^2+30y-27=0

Solution for 5y^2+30y-27=0 equation:

5y^2+30y-27=0

a = 5; b = 30; c = -27;
Δ = b2-4ac
Δ = 302-4·5·(-27)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{10}}{2*5}=\frac{-30-12\sqrt{10}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{10}}{2*5}=\frac{-30+12\sqrt{10}}{10}
$