-9y^2+15=-8y+6

Solution for -9y^2+15=-8y+6 equation:

-9y^2+15=-8y+6

We move all terms to the left:

-9y^2+15-(-8y+6)=0

We get rid of parentheses

-9y^2+8y-6+15=0

We add all the numbers together, and all the variables

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

a = -9; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-9)·9
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{97}}{2*-9}=\frac{-8-2\sqrt{97}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{97}}{2*-9}=\frac{-8+2\sqrt{97}}{-18}
$