7/5u-1/5=-2/3u-1

Solution for 7/5u-1/5=-2/3u-1 equation:

7/5u-1/5=-2/3u-1

We move all terms to the left:

7/5u-1/5-(-2/3u-1)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 3u-1)!=0

u∈R


We get rid of parentheses

7/5u+2/3u+1-1/5=0

We calculate fractions


21u/375u^2+250u/375u^2+(-3u)/375u^2+1=0

We multiply all the terms by the denominator


21u+250u+(-3u)+1*375u^2=0

We add all the numbers together, and all the variables

271u+(-3u)+1*375u^2=0

Wy multiply elements

375u^2+271u+(-3u)=0

We get rid of parentheses

375u^2+271u-3u=0

We add all the numbers together, and all the variables

375u^2+268u=0

a = 375; b = 268; c = 0;
Δ = b2-4ac
Δ = 2682-4·375·0
Δ = 71824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{71824}=268$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(268)-268}{2*375}=\frac{-536}{750}
=-268/375
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(268)+268}{2*375}=\frac{0}{750}
=0
$