-3/5u+5/3=-1/3u-6

Solution for -3/5u+5/3=-1/3u-6 equation:

-3/5u+5/3=-1/3u-6

We move all terms to the left:

-3/5u+5/3-(-1/3u-6)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 3u-6)!=0

u∈R


We get rid of parentheses

-3/5u+1/3u+6+5/3=0

We calculate fractions


(-81u)/135u^2+5u/135u^2+25u/135u^2+6=0

We multiply all the terms by the denominator


(-81u)+5u+25u+6*135u^2=0

We add all the numbers together, and all the variables

30u+(-81u)+6*135u^2=0

Wy multiply elements

810u^2+30u+(-81u)=0

We get rid of parentheses

810u^2+30u-81u=0

We add all the numbers together, and all the variables

810u^2-51u=0

a = 810; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·810·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*810}=\frac{0}{1620}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*810}=\frac{102}{1620}
=17/270
$