2y^2-8=14-9y

Solution for 2y^2-8=14-9y equation:

2y^2-8=14-9y

We move all terms to the left:

2y^2-8-(14-9y)=0

We add all the numbers together, and all the variables

2y^2-(-9y+14)-8=0

We get rid of parentheses

2y^2+9y-14-8=0

We add all the numbers together, and all the variables

2y^2+9y-22=0

a = 2; b = 9; c = -22;
Δ = b2-4ac
Δ = 92-4·2·(-22)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{257}}{2*2}=\frac{-9-\sqrt{257}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{257}}{2*2}=\frac{-9+\sqrt{257}}{4}
$