-5(v+2)3v+7=7v+12

Solution for -5(v+2)3v+7=7v+12 equation:

-5(v+2)3v+7=7v+12

We move all terms to the left:

-5(v+2)3v+7-(7v+12)=0

We multiply parentheses

-15v^2-30v-(7v+12)+7=0

We get rid of parentheses

-15v^2-30v-7v-12+7=0

We add all the numbers together, and all the variables

-15v^2-37v-5=0

a = -15; b = -37; c = -5;
Δ = b2-4ac
Δ = -372-4·(-15)·(-5)
Δ = 1069
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1069}}{2*-15}=\frac{37-\sqrt{1069}}{-30}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1069}}{2*-15}=\frac{37+\sqrt{1069}}{-30}
$