7/3u+2/5u=1

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

7/3u+2/5u=1

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R


We calculate fractions


35u/15u^2+6u/15u^2-1=0

We multiply all the terms by the denominator


35u+6u-1*15u^2=0

We add all the numbers together, and all the variables

41u-1*15u^2=0

Wy multiply elements

-15u^2+41u=0

a = -15; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-15)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-15}=\frac{-82}{-30}
=2+11/15
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-15}=\frac{0}{-30}
=0
$