6y2-3y=9

Solution for 6y2-3y=9 equation:

6y^2-3y=9

We move all terms to the left:

6y^2-3y-(9)=0

a = 6; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·6·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*6}=\frac{-12}{12}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*6}=\frac{18}{12}
=1+1/2
$