9y2+12y-14=0

Solution for 9y2+12y-14=0 equation:

9y^2+12y-14=0

a = 9; b = 12; c = -14;
Δ = b2-4ac
Δ = 122-4·9·(-14)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18\sqrt{2}}{2*9}=\frac{-12-18\sqrt{2}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18\sqrt{2}}{2*9}=\frac{-12+18\sqrt{2}}{18}
$