7/2u-5/3u=1

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

7/2u-5/3u=1

We move all terms to the left:

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


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R


We calculate fractions


21u/6u^2+(-10u)/6u^2-1=0

We multiply all the terms by the denominator


21u+(-10u)-1*6u^2=0

Wy multiply elements

-6u^2+21u+(-10u)=0

We get rid of parentheses

-6u^2+21u-10u=0

We add all the numbers together, and all the variables

-6u^2+11u=0

a = -6; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-6)·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*-6}=\frac{-22}{-12}
=1+5/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-6}=\frac{0}{-12}
=0
$