34y-3y^2=90

Solution for 34y-3y^2=90 equation:

34y-3y^2=90

We move all terms to the left:

34y-3y^2-(90)=0

a = -3; b = 34; c = -90;
Δ = b2-4ac
Δ = 342-4·(-3)·(-90)
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{-(34)-2\sqrt{19}}{2*-3}=\frac{-34-2\sqrt{19}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{19}}{2*-3}=\frac{-34+2\sqrt{19}}{-6}
$