6y^2+8y-9=2

Solution for 6y^2+8y-9=2 equation:

6y^2+8y-9=2

We move all terms to the left:

6y^2+8y-9-(2)=0

We add all the numbers together, and all the variables

6y^2+8y-11=0

a = 6; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·6·(-11)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{82}}{2*6}=\frac{-8-2\sqrt{82}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{82}}{2*6}=\frac{-8+2\sqrt{82}}{12}
$