(2/(3u))+(7/(5u))=1

Solution for (2/(3u))+(7/(5u))=1 equation:

(2/(3u))+(7/(5u))=1

We move all terms to the left:

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


Domain of the equation: 3u)!=0

u!=0/1

u!=0

u∈R



Domain of the equation: 5u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10u/15u^2+21u/15u^2-1=0

We multiply all the terms by the denominator


10u+21u-1*15u^2=0

We add all the numbers together, and all the variables

31u-1*15u^2=0

Wy multiply elements

-15u^2+31u=0

a = -15; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-15)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-15}=\frac{-62}{-30}
=2+1/15
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-15}=\frac{0}{-30}
=0
$