5/7u-3/2u=1

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

5/7u-3/2u=1

We move all terms to the left:

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


Domain of the equation: 7u!=0

u!=0/7

u!=0

u∈R



Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R


We calculate fractions


10u/14u^2+(-21u)/14u^2-1=0

We multiply all the terms by the denominator


10u+(-21u)-1*14u^2=0

Wy multiply elements

-14u^2+10u+(-21u)=0

We get rid of parentheses

-14u^2+10u-21u=0

We add all the numbers together, and all the variables

-14u^2-11u=0

a = -14; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-14)·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*-14}=\frac{0}{-28}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-14}=\frac{22}{-28}
=-11/14
$