-7/5u-5/3=4/3u-2

Solution for -7/5u-5/3=4/3u-2 equation:

-7/5u-5/3=4/3u-2

We move all terms to the left:

-7/5u-5/3-(4/3u-2)=0


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



Domain of the equation: 3u-2)!=0

u∈R


We get rid of parentheses

-7/5u-4/3u+2-5/3=0

We calculate fractions


(-189u)/135u^2+(-20u)/135u^2+(-25u)/135u^2+2=0

We multiply all the terms by the denominator


(-189u)+(-20u)+(-25u)+2*135u^2=0

Wy multiply elements

270u^2+(-189u)+(-20u)+(-25u)=0

We get rid of parentheses

270u^2-189u-20u-25u=0

We add all the numbers together, and all the variables

270u^2-234u=0

a = 270; b = -234; c = 0;
Δ = b2-4ac
Δ = -2342-4·270·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-234}{2*270}=\frac{0}{540}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+234}{2*270}=\frac{468}{540}
=13/15
$