-7/3u+1/2=1/6u-2

Solution for -7/3u+1/2=1/6u-2 equation:

-7/3u+1/2=1/6u-2

We move all terms to the left:

-7/3u+1/2-(1/6u-2)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 6u-2)!=0

u∈R


We get rid of parentheses

-7/3u-1/6u+2+1/2=0

We calculate fractions


108u^2/72u^2+(-168u)/72u^2+(-12u)/72u^2+2=0

We multiply all the terms by the denominator


108u^2+(-168u)+(-12u)+2*72u^2=0

Wy multiply elements

108u^2+144u^2+(-168u)+(-12u)=0

We get rid of parentheses

108u^2+144u^2-168u-12u=0

We add all the numbers together, and all the variables

252u^2-180u=0

a = 252; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·252·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*252}=\frac{0}{504}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*252}=\frac{360}{504}
=5/7
$