-7/3u+1/3=-3/2u-5

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

-7/3u+1/3=-3/2u-5

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


(-14u)/54u^2+81u/54u^2+2u/54u^2+5=0

We multiply all the terms by the denominator


(-14u)+81u+2u+5*54u^2=0

We add all the numbers together, and all the variables

83u+(-14u)+5*54u^2=0

Wy multiply elements

270u^2+83u+(-14u)=0

We get rid of parentheses

270u^2+83u-14u=0

We add all the numbers together, and all the variables

270u^2+69u=0

a = 270; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·270·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*270}=\frac{-138}{540}
=-23/90
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*270}=\frac{0}{540}
=0
$