5/4u-4/3=-1/3u-4

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Solution for 5/4u-4/3=-1/3u-4 equation:



5/4u-4/3=-1/3u-4
We move all terms to the left:
5/4u-4/3-(-1/3u-4)=0
Domain of the equation: 4u!=0
u!=0/4
u!=0
u∈R
Domain of the equation: 3u-4)!=0
u∈R
We get rid of parentheses
5/4u+1/3u+4-4/3=0
We calculate fractions
135u/108u^2+4u/108u^2+(-16u)/108u^2+4=0
We multiply all the terms by the denominator
135u+4u+(-16u)+4*108u^2=0
We add all the numbers together, and all the variables
139u+(-16u)+4*108u^2=0
Wy multiply elements
432u^2+139u+(-16u)=0
We get rid of parentheses
432u^2+139u-16u=0
We add all the numbers together, and all the variables
432u^2+123u=0
a = 432; b = 123; c = 0;
Δ = b2-4ac
Δ = 1232-4·432·0
Δ = 15129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15129}=123$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(123)-123}{2*432}=\frac{-246}{864} =-41/144 $
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(123)+123}{2*432}=\frac{0}{864} =0 $

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