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

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

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

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 5u-7)!=0

u∈R


We get rid of parentheses

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

We calculate fractions


(-625u)/375u^2+21u/375u^2+6u/375u^2+7=0

We multiply all the terms by the denominator


(-625u)+21u+6u+7*375u^2=0

We add all the numbers together, and all the variables

27u+(-625u)+7*375u^2=0

Wy multiply elements

2625u^2+27u+(-625u)=0

We get rid of parentheses

2625u^2+27u-625u=0

We add all the numbers together, and all the variables

2625u^2-598u=0

a = 2625; b = -598; c = 0;
Δ = b2-4ac
Δ = -5982-4·2625·0
Δ = 357604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{357604}=598$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-598)-598}{2*2625}=\frac{0}{5250}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-598)+598}{2*2625}=\frac{1196}{5250}
=598/2625
$