31/3x+8=42/5x-8

Solution for 31/3x+8=42/5x-8 equation:

31/3x+8=42/5x-8

We move all terms to the left:

31/3x+8-(42/5x-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

31/3x-42/5x+8+8=0

We calculate fractions


155x/15x^2+(-126x)/15x^2+8+8=0

We add all the numbers together, and all the variables

155x/15x^2+(-126x)/15x^2+16=0

We multiply all the terms by the denominator


155x+(-126x)+16*15x^2=0

Wy multiply elements

240x^2+155x+(-126x)=0

We get rid of parentheses

240x^2+155x-126x=0

We add all the numbers together, and all the variables

240x^2+29x=0

a = 240; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·240·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*240}=\frac{-58}{480}
=-29/240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*240}=\frac{0}{480}
=0
$