5/2v-7/5=-2/5v-6

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

5/2v-7/5=-2/5v-6

We move all terms to the left:

5/2v-7/5-(-2/5v-6)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 5v-6)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


625v/250v^2+4v/250v^2+(-14v)/250v^2+6=0

We multiply all the terms by the denominator


625v+4v+(-14v)+6*250v^2=0

We add all the numbers together, and all the variables

629v+(-14v)+6*250v^2=0

Wy multiply elements

1500v^2+629v+(-14v)=0

We get rid of parentheses

1500v^2+629v-14v=0

We add all the numbers together, and all the variables

1500v^2+615v=0

a = 1500; b = 615; c = 0;
Δ = b2-4ac
Δ = 6152-4·1500·0
Δ = 378225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{378225}=615$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(615)-615}{2*1500}=\frac{-1230}{3000}
=-41/100
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(615)+615}{2*1500}=\frac{0}{3000}
=0
$