-12v+18=2v^2

Solution for -12v+18=2v^2 equation:

-12v+18=2v^2

We move all terms to the left:

-12v+18-(2v^2)=0

determiningTheFunctionDomain
-2v^2-12v+18=0

a = -2; b = -12; c = +18;
Δ = b2-4ac
Δ = -122-4·(-2)·18
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*-2}=\frac{12-12\sqrt{2}}{-4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*-2}=\frac{12+12\sqrt{2}}{-4}
$