5+2v=-3/2v-2

Solution for 5+2v=-3/2v-2 equation:

5+2v=-3/2v-2

We move all terms to the left:

5+2v-(-3/2v-2)=0


Domain of the equation: 2v-2)!=0

v∈R


We get rid of parentheses

2v+3/2v+2+5=0

We multiply all the terms by the denominator


2v*2v+2*2v+5*2v+3=0

Wy multiply elements

4v^2+4v+10v+3=0

We add all the numbers together, and all the variables

4v^2+14v+3=0

a = 4; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·4·3
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{37}}{2*4}=\frac{-14-2\sqrt{37}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{37}}{2*4}=\frac{-14+2\sqrt{37}}{8}
$