3/7u+2/5u=1

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

3/7u+2/5u=1

We move all terms to the left:

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


Domain of the equation: 7u!=0

u!=0/7

u!=0

u∈R



Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R


We calculate fractions


15u/35u^2+14u/35u^2-1=0

We multiply all the terms by the denominator


15u+14u-1*35u^2=0

We add all the numbers together, and all the variables

29u-1*35u^2=0

Wy multiply elements

-35u^2+29u=0

a = -35; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-35)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-35}=\frac{-58}{-70}
=29/35
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-35}=\frac{0}{-70}
=0
$