-6/5u-7/3=7/3u-1

Solution for -6/5u-7/3=7/3u-1 equation:

-6/5u-7/3=7/3u-1

We move all terms to the left:

-6/5u-7/3-(7/3u-1)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 3u-1)!=0

u∈R


We get rid of parentheses

-6/5u-7/3u+1-7/3=0

We calculate fractions


(-162u)/135u^2+(-35u)/135u^2+(-35u)/135u^2+1=0

We multiply all the terms by the denominator


(-162u)+(-35u)+(-35u)+1*135u^2=0

Wy multiply elements

135u^2+(-162u)+(-35u)+(-35u)=0

We get rid of parentheses

135u^2-162u-35u-35u=0

We add all the numbers together, and all the variables

135u^2-232u=0

a = 135; b = -232; c = 0;
Δ = b2-4ac
Δ = -2322-4·135·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-232}{2*135}=\frac{0}{270}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+232}{2*135}=\frac{464}{270}
=1+97/135
$