3y2-51y=9

Solution for 3y2-51y=9 equation:

3y^2-51y=9

We move all terms to the left:

3y^2-51y-(9)=0

a = 3; b = -51; c = -9;
Δ = b2-4ac
Δ = -512-4·3·(-9)
Δ = 2709
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:

$\sqrt{\Delta}=\sqrt{2709}=\sqrt{9*301}=\sqrt{9}*\sqrt{301}=3\sqrt{301}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{301}}{2*3}=\frac{51-3\sqrt{301}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{301}}{2*3}=\frac{51+3\sqrt{301}}{6}
$