6y^2-7y=9

Solution for 6y^2-7y=9 equation:

6y^2-7y=9

We move all terms to the left:

6y^2-7y-(9)=0

a = 6; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·6·(-9)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{265}}{2*6}=\frac{7-\sqrt{265}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{265}}{2*6}=\frac{7+\sqrt{265}}{12}
$