1/5x+8-3/5=1/3x-3

Solution for 1/5x+8-3/5=1/3x-3 equation:

1/5x+8-3/5=1/3x-3

We move all terms to the left:

1/5x+8-3/5-(1/3x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

1/5x-1/3x+3+8-3/5=0

We calculate fractions


3x/375x^2+(-125x)/375x^2+(-9x)/375x^2+3+8=0

We add all the numbers together, and all the variables

3x/375x^2+(-125x)/375x^2+(-9x)/375x^2+11=0

We multiply all the terms by the denominator


3x+(-125x)+(-9x)+11*375x^2=0

Wy multiply elements

4125x^2+3x+(-125x)+(-9x)=0

We get rid of parentheses

4125x^2+3x-125x-9x=0

We add all the numbers together, and all the variables

4125x^2-131x=0

a = 4125; b = -131; c = 0;
Δ = b2-4ac
Δ = -1312-4·4125·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-131)-131}{2*4125}=\frac{0}{8250}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131)+131}{2*4125}=\frac{262}{8250}
=131/4125
$