34y-2y^2=21

Solution for 34y-2y^2=21 equation:

34y-2y^2=21

We move all terms to the left:

34y-2y^2-(21)=0

a = -2; b = 34; c = -21;
Δ = b2-4ac
Δ = 342-4·(-2)·(-21)
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{247}}{2*-2}=\frac{-34-2\sqrt{247}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{247}}{2*-2}=\frac{-34+2\sqrt{247}}{-4}
$