-5/2v+7/2=-1/3v-6

Solution for -5/2v+7/2=-1/3v-6 equation:

-5/2v+7/2=-1/3v-6

We move all terms to the left:

-5/2v+7/2-(-1/3v-6)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v-6)!=0

v∈R


We get rid of parentheses

-5/2v+1/3v+6+7/2=0

We calculate fractions


(-15v)/24v^2+8v/24v^2+21v/24v^2+6=0

We multiply all the terms by the denominator


(-15v)+8v+21v+6*24v^2=0

We add all the numbers together, and all the variables

29v+(-15v)+6*24v^2=0

Wy multiply elements

144v^2+29v+(-15v)=0

We get rid of parentheses

144v^2+29v-15v=0

We add all the numbers together, and all the variables

144v^2+14v=0

a = 144; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·144·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*144}=\frac{-28}{288}
=-7/72
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*144}=\frac{0}{288}
=0
$