-3/v-3=1/4v-12+2

Solution for -3/v-3=1/4v-12+2 equation:

-3/v-3=1/4v-12+2

We move all terms to the left:

-3/v-3-(1/4v-12+2)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: 4v-12+2)!=0

We move all terms containing v to the left, all other terms to the right

4v+2)!=12

v∈R


We add all the numbers together, and all the variables

-3/v-(1/4v-10)-3=0

We get rid of parentheses

-3/v-1/4v+10-3=0

We calculate fractions


(-12v)/4v^2+(-v)/4v^2+10-3=0

We add all the numbers together, and all the variables

(-12v)/4v^2+(-1v)/4v^2+10-3=0

We add all the numbers together, and all the variables

(-12v)/4v^2+(-1v)/4v^2+7=0

We multiply all the terms by the denominator


(-12v)+(-1v)+7*4v^2=0

Wy multiply elements

28v^2+(-12v)+(-1v)=0

We get rid of parentheses

28v^2-12v-1v=0

We add all the numbers together, and all the variables

28v^2-13v=0

a = 28; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·28·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*28}=\frac{0}{56}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*28}=\frac{26}{56}
=13/28
$