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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(-13y)+(6y^2+y)-9=0

We get rid of parentheses

6y^2-13y+y-9=0

We add all the numbers together, and all the variables

6y^2-12y-9=0

a = 6; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·6·(-9)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*6}=\frac{12-6\sqrt{10}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*6}=\frac{12+6\sqrt{10}}{12}
$