5x/2x=2x/16

Solution for 5x/2x=2x/16 equation:

5x/2x=2x/16

We move all terms to the left:

5x/2x-(2x/16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x/2x-(+2x/16)=0

We get rid of parentheses

5x/2x-2x/16=0

We calculate fractions


(-4x^2)/32x+80x/32x=0

We multiply all the terms by the denominator


(-4x^2)+80x=0

We get rid of parentheses

-4x^2+80x=0

a = -4; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-4)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-4}=\frac{-160}{-8}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-4}=\frac{0}{-8}
=0
$