V(x)=12x^2+7x-12

Solution for V(x)=12x^2+7x-12 equation:

(V)=12V^2+7V-12

We move all terms to the left:

(V)-(12V^2+7V-12)=0

We get rid of parentheses

-12V^2+V-7V+12=0

We add all the numbers together, and all the variables

-12V^2-6V+12=0

a = -12; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-12)·12
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{17}}{2*-12}=\frac{6-6\sqrt{17}}{-24}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{17}}{2*-12}=\frac{6+6\sqrt{17}}{-24}
$