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

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

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

We move all terms to the left:

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


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: 2v-6)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


(-12v)/250v^2+125v/250v^2+6v/250v^2+6=0

We multiply all the terms by the denominator


(-12v)+125v+6v+6*250v^2=0

We add all the numbers together, and all the variables

131v+(-12v)+6*250v^2=0

Wy multiply elements

1500v^2+131v+(-12v)=0

We get rid of parentheses

1500v^2+131v-12v=0

We add all the numbers together, and all the variables

1500v^2+119v=0

a = 1500; b = 119; c = 0;
Δ = b2-4ac
Δ = 1192-4·1500·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-119}{2*1500}=\frac{-238}{3000}
=-119/1500
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+119}{2*1500}=\frac{0}{3000}
=0
$