5/3u+7/2u=1

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

5/3u+7/2u=1

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

31u-1*6u^2=0

Wy multiply elements

-6u^2+31u=0

a = -6; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-6)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-6}=\frac{-62}{-12}
=5+1/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-6}=\frac{0}{-12}
=0
$