4/5u-1/5=-1/3u-2

Solution for 4/5u-1/5=-1/3u-2 equation:

4/5u-1/5=-1/3u-2

We move all terms to the left:

4/5u-1/5-(-1/3u-2)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 3u-2)!=0

u∈R


We get rid of parentheses

4/5u+1/3u+2-1/5=0

We calculate fractions


12u/375u^2+125u/375u^2+(-3u)/375u^2+2=0

We multiply all the terms by the denominator


12u+125u+(-3u)+2*375u^2=0

We add all the numbers together, and all the variables

137u+(-3u)+2*375u^2=0

Wy multiply elements

750u^2+137u+(-3u)=0

We get rid of parentheses

750u^2+137u-3u=0

We add all the numbers together, and all the variables

750u^2+134u=0

a = 750; b = 134; c = 0;
Δ = b2-4ac
Δ = 1342-4·750·0
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-134}{2*750}=\frac{-268}{1500}
=-67/375
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+134}{2*750}=\frac{0}{1500}
=0
$