7/3u-2/5u=1

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

7/3u-2/5u=1

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R


We calculate fractions


35u/15u^2+(-6u)/15u^2-1=0

We multiply all the terms by the denominator


35u+(-6u)-1*15u^2=0

Wy multiply elements

-15u^2+35u+(-6u)=0

We get rid of parentheses

-15u^2+35u-6u=0

We add all the numbers together, and all the variables

-15u^2+29u=0

a = -15; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-15)·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*-15}=\frac{-58}{-30}
=1+14/15
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-15}=\frac{0}{-30}
=0
$