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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

7/4x+2/8x+2/5=0

We calculate fractions


512x^2/800x^2+1400x/800x^2+200x/800x^2=0

We multiply all the terms by the denominator


512x^2+1400x+200x=0

We add all the numbers together, and all the variables

512x^2+1600x=0

a = 512; b = 1600; c = 0;
Δ = b2-4ac
Δ = 16002-4·512·0
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-1600}{2*512}=\frac{-3200}{1024}
=-3+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+1600}{2*512}=\frac{0}{1024}
=0
$