-7/3v+4/3=5/2v-2

Solution for -7/3v+4/3=5/2v-2 equation:

-7/3v+4/3=5/2v-2

We move all terms to the left:

-7/3v+4/3-(5/2v-2)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



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

v∈R


We get rid of parentheses

-7/3v-5/2v+2+4/3=0

We calculate fractions


(-14v)/54v^2+(-135v)/54v^2+8v/54v^2+2=0

We multiply all the terms by the denominator


(-14v)+(-135v)+8v+2*54v^2=0

We add all the numbers together, and all the variables

8v+(-14v)+(-135v)+2*54v^2=0

Wy multiply elements

108v^2+8v+(-14v)+(-135v)=0

We get rid of parentheses

108v^2+8v-14v-135v=0

We add all the numbers together, and all the variables

108v^2-141v=0

a = 108; b = -141; c = 0;
Δ = b2-4ac
Δ = -1412-4·108·0
Δ = 19881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19881}=141$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-141)-141}{2*108}=\frac{0}{216}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-141)+141}{2*108}=\frac{282}{216}
=1+11/36
$