-2y^2+5=6y

Solution for -2y^2+5=6y equation:

-2y^2+5=6y

We move all terms to the left:

-2y^2+5-(6y)=0

a = -2; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-2)·5
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*-2}=\frac{6-2\sqrt{19}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*-2}=\frac{6+2\sqrt{19}}{-4}
$