4y^2+9y-81=0

Solution for 4y^2+9y-81=0 equation:

4y^2+9y-81=0

a = 4; b = 9; c = -81;
Δ = b2-4ac
Δ = 92-4·4·(-81)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{17}}{2*4}=\frac{-9-9\sqrt{17}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{17}}{2*4}=\frac{-9+9\sqrt{17}}{8}
$