x/2x+16=4x-8

Solution for x/2x+16=4x-8 equation:

x/2x+16=4x-8

We move all terms to the left:

x/2x+16-(4x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-4x+8+16=0

We multiply all the terms by the denominator


x-4x*2x+8*2x+16*2x=0

Wy multiply elements

-8x^2+x+16x+32x=0

We add all the numbers together, and all the variables

-8x^2+49x=0

a = -8; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-8)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-8}=\frac{-98}{-16}
=6+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-8}=\frac{0}{-16}
=0
$