-(7/4v-12)+2=5/v-3

Solution for -(7/4v-12)+2=5/v-3 equation:

-(7/4v-12)+2=5/v-3

We move all terms to the left:

-(7/4v-12)+2-(5/v-3)=0


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

v∈R



Domain of the equation: v-3)!=0

v∈R


We get rid of parentheses

-7/4v-5/v+12+3+2=0

We calculate fractions


(-7v)/4v^2+(-20v)/4v^2+12+3+2=0

We add all the numbers together, and all the variables

(-7v)/4v^2+(-20v)/4v^2+17=0

We multiply all the terms by the denominator


(-7v)+(-20v)+17*4v^2=0

Wy multiply elements

68v^2+(-7v)+(-20v)=0

We get rid of parentheses

68v^2-7v-20v=0

We add all the numbers together, and all the variables

68v^2-27v=0

a = 68; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·68·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*68}=\frac{0}{136}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*68}=\frac{54}{136}
=27/68
$