2y^2+3y-144=0

Solution for 2y^2+3y-144=0 equation:

2y^2+3y-144=0

a = 2; b = 3; c = -144;
Δ = b2-4ac
Δ = 32-4·2·(-144)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{129}}{2*2}=\frac{-3-3\sqrt{129}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{129}}{2*2}=\frac{-3+3\sqrt{129}}{4}
$