9v2+6v-2=7

Solution for 9v2+6v-2=7 equation:

9v^2+6v-2=7

We move all terms to the left:

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

We add all the numbers together, and all the variables

9v^2+6v-9=0

a = 9; b = 6; c = -9;
Δ = b2-4ac
Δ = 62-4·9·(-9)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{10}}{2*9}=\frac{-6-6\sqrt{10}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{10}}{2*9}=\frac{-6+6\sqrt{10}}{18}
$