14y^2+16y=9

Solution for 14y^2+16y=9 equation:

14y^2+16y=9

We move all terms to the left:

14y^2+16y-(9)=0

a = 14; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·14·(-9)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{190}}{2*14}=\frac{-16-2\sqrt{190}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{190}}{2*14}=\frac{-16+2\sqrt{190}}{28}
$