-7/3u-7/3=6/5u-2

Solution for -7/3u-7/3=6/5u-2 equation:

-7/3u-7/3=6/5u-2

We move all terms to the left:

-7/3u-7/3-(6/5u-2)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 5u-2)!=0

u∈R


We get rid of parentheses

-7/3u-6/5u+2-7/3=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

270u^2+(-35u)+(-162u)+(-35u)=0

We get rid of parentheses

270u^2-35u-162u-35u=0

We add all the numbers together, and all the variables

270u^2-232u=0

a = 270; b = -232; c = 0;
Δ = b2-4ac
Δ = -2322-4·270·0
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*270}=\frac{0}{540}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+232}{2*270}=\frac{464}{540}
=116/135
$