1/2v+11/12-11/4v=-5/12

Solution for 1/2v+11/12-11/4v=-5/12 equation:

1/2v+11/12-11/4v=-5/12

We move all terms to the left:

1/2v+11/12-11/4v-(-5/12)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R


We get rid of parentheses

1/2v-11/4v+11/12+5/12=0

We calculate fractions


48v/96v^2+(-264v)/96v^2+(160v^2+11)/96v^2=0

We multiply all the terms by the denominator


48v+(-264v)+(160v^2+11)=0

We get rid of parentheses

160v^2+48v-264v+11=0

We add all the numbers together, and all the variables

160v^2-216v+11=0

a = 160; b = -216; c = +11;
Δ = b2-4ac
Δ = -2162-4·160·11
Δ = 39616
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:

$\sqrt{\Delta}=\sqrt{39616}=\sqrt{64*619}=\sqrt{64}*\sqrt{619}=8\sqrt{619}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-8\sqrt{619}}{2*160}=\frac{216-8\sqrt{619}}{320}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+8\sqrt{619}}{2*160}=\frac{216+8\sqrt{619}}{320}
$