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

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

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

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 5u-2)!=0

u∈R


We get rid of parentheses

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

We calculate fractions


300u^2/375u^2+(-500u)/375u^2+150u/375u^2+2=0

We multiply all the terms by the denominator


300u^2+(-500u)+150u+2*375u^2=0

We add all the numbers together, and all the variables

300u^2+150u+(-500u)+2*375u^2=0

Wy multiply elements

300u^2+750u^2+150u+(-500u)=0

We get rid of parentheses

300u^2+750u^2+150u-500u=0

We add all the numbers together, and all the variables

1050u^2-350u=0

a = 1050; b = -350; c = 0;
Δ = b2-4ac
Δ = -3502-4·1050·0
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-350}{2*1050}=\frac{0}{2100}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+350}{2*1050}=\frac{700}{2100}
=1/3
$