V(x)=(x+3)(x-2)

Solution for V(x)=(x+3)(x-2) equation:

(V)=(V+3)(V-2)

We move all terms to the left:

(V)-((V+3)(V-2))=0

We multiply parentheses ..

-((+V^2-2V+3V-6))+V=0


We calculate terms in parentheses: -((+V^2-2V+3V-6)), so:

(+V^2-2V+3V-6)

We get rid of parentheses

V^2-2V+3V-6

We add all the numbers together, and all the variables

V^2+V-6

Back to the equation:

-(V^2+V-6)


We add all the numbers together, and all the variables

V-(V^2+V-6)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1V^2+6=0

a = -1; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-1)·6
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-1}=\frac{0-2\sqrt{6}}{-2}
=-\frac{2\sqrt{6}}{-2}
=-\frac{\sqrt{6}}{-1}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-1}=\frac{0+2\sqrt{6}}{-2}
=\frac{2\sqrt{6}}{-2}
=\frac{\sqrt{6}}{-1}
$