2/u-3/7u=1

Solution for 2/u-3/7u=1 equation:

2/u-3/7u=1

We move all terms to the left:

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


Domain of the equation: u!=0

u∈R



Domain of the equation: 7u!=0

u!=0/7

u!=0

u∈R


We calculate fractions


14u/7u^2+(-3u)/7u^2-1=0

We multiply all the terms by the denominator


14u+(-3u)-1*7u^2=0

Wy multiply elements

-7u^2+14u+(-3u)=0

We get rid of parentheses

-7u^2+14u-3u=0

We add all the numbers together, and all the variables

-7u^2+11u=0

a = -7; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-7)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-7}=\frac{-22}{-14}
=1+4/7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-7}=\frac{0}{-14}
=0
$