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

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
$