34-2/3x=1/5x+8

Solution for 34-2/3x=1/5x+8 equation:

34-2/3x=1/5x+8

We move all terms to the left:

34-2/3x-(1/5x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+8)!=0

x∈R


We get rid of parentheses

-2/3x-1/5x-8+34=0

We calculate fractions


(-10x)/15x^2+(-3x)/15x^2-8+34=0

We add all the numbers together, and all the variables

(-10x)/15x^2+(-3x)/15x^2+26=0

We multiply all the terms by the denominator


(-10x)+(-3x)+26*15x^2=0

Wy multiply elements

390x^2+(-10x)+(-3x)=0

We get rid of parentheses

390x^2-10x-3x=0

We add all the numbers together, and all the variables

390x^2-13x=0

a = 390; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·390·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*390}=\frac{0}{780}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*390}=\frac{26}{780}
=1/30
$