6y=8y^2-15

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

6y=8y^2-15

We move all terms to the left:

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

We get rid of parentheses

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

a = -8; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-8)·15
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{129}}{2*-8}=\frac{-6-2\sqrt{129}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{129}}{2*-8}=\frac{-6+2\sqrt{129}}{-16}
$