3/4v=3v+24

Solution for 3/4v=3v+24 equation:

3/4v=3v+24

We move all terms to the left:

3/4v-(3v+24)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R


We get rid of parentheses

3/4v-3v-24=0

We multiply all the terms by the denominator


-3v*4v-24*4v+3=0

Wy multiply elements

-12v^2-96v+3=0

a = -12; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·(-12)·3
Δ = 9360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9360}=\sqrt{144*65}=\sqrt{144}*\sqrt{65}=12\sqrt{65}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{65}}{2*-12}=\frac{96-12\sqrt{65}}{-24}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{65}}{2*-12}=\frac{96+12\sqrt{65}}{-24}
$