(3x+5/8x)(2x)=x

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

(3x+5/8x)(2x)=x

We move all terms to the left:

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


Domain of the equation: 8x)2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(+3x+5/8x)2x=0

We multiply parentheses

6x^2+10x^2-1x=0

We add all the numbers together, and all the variables

16x^2-1x=0

a = 16; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·16·0
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*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*16}=\frac{2}{32}
=1/16
$