2/5x-3=4/8x+7

Solution for 2/5x-3=4/8x+7 equation:

2/5x-3=4/8x+7

We move all terms to the left:

2/5x-3-(4/8x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x+7)!=0

x∈R


We get rid of parentheses

2/5x-4/8x-7-3=0

We calculate fractions


16x/40x^2+(-20x)/40x^2-7-3=0

We add all the numbers together, and all the variables

16x/40x^2+(-20x)/40x^2-10=0

We multiply all the terms by the denominator


16x+(-20x)-10*40x^2=0

Wy multiply elements

-400x^2+16x+(-20x)=0

We get rid of parentheses

-400x^2+16x-20x=0

We add all the numbers together, and all the variables

-400x^2-4x=0

a = -400; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-400)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-400}=\frac{0}{-800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-400}=\frac{8}{-800}
=-1/100
$