7/4x+205=-2/8x

Solution for 7/4x+205=-2/8x equation:

7/4x+205=-2/8x

We move all terms to the left:

7/4x+205-(-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+205=0

We calculate fractions


56x/32x^2+8x/32x^2+205=0

We multiply all the terms by the denominator


56x+8x+205*32x^2=0

We add all the numbers together, and all the variables

64x+205*32x^2=0

Wy multiply elements

6560x^2+64x=0

a = 6560; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·6560·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*6560}=\frac{-128}{13120}
=-2/205
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*6560}=\frac{0}{13120}
=0
$