2/5x+8=3/7x

Solution for 2/5x+8=3/7x equation:

2/5x+8=3/7x

We move all terms to the left:

2/5x+8-(3/7x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(+3/7x)+8=0

We get rid of parentheses

2/5x-3/7x+8=0

We calculate fractions


14x/35x^2+(-15x)/35x^2+8=0

We multiply all the terms by the denominator


14x+(-15x)+8*35x^2=0

Wy multiply elements

280x^2+14x+(-15x)=0

We get rid of parentheses

280x^2+14x-15x=0

We add all the numbers together, and all the variables

280x^2-1x=0

a = 280; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·280·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*280}=\frac{0}{560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*280}=\frac{2}{560}
=1/280
$