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

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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 $

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