-3/4v-24+1=7/v-6

Solution for -3/4v-24+1=7/v-6 equation:

-3/4v-24+1=7/v-6

We move all terms to the left:

-3/4v-24+1-(7/v-6)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



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

v∈R


We add all the numbers together, and all the variables

-3/4v-(7/v-6)-23=0

We get rid of parentheses

-3/4v-7/v+6-23=0

We calculate fractions


(-3v)/4v^2+(-28v)/4v^2+6-23=0

We add all the numbers together, and all the variables

(-3v)/4v^2+(-28v)/4v^2-17=0

We multiply all the terms by the denominator


(-3v)+(-28v)-17*4v^2=0

Wy multiply elements

-68v^2+(-3v)+(-28v)=0

We get rid of parentheses

-68v^2-3v-28v=0

We add all the numbers together, and all the variables

-68v^2-31v=0

a = -68; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·(-68)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*-68}=\frac{0}{-136}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*-68}=\frac{62}{-136}
=-31/68
$