C.5/2x=2.5x

Solution for C.5/2x=2.5x equation:

.5/2C=2.5C

We move all terms to the left:

.5/2C-(2.5C)=0


Domain of the equation: 2C!=0

C!=0/2

C!=0

C∈R


We add all the numbers together, and all the variables

.5/2C-(+2.5C)=0

We get rid of parentheses

.5/2C-2.5C=0

We multiply all the terms by the denominator


-(2.5C)*2C+.5=0

We add all the numbers together, and all the variables

-(+2.5C)*2C+.5=0

We add all the numbers together, and all the variables

-(+2.5C)*2C+0.5=0

We multiply parentheses

-4C^2+0.5=0

a = -4; b = 0; c = +0.5;
Δ = b2-4ac
Δ = 02-4·(-4)·0.5
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-4}=\frac{0-2\sqrt{2}}{-8}
=-\frac{2\sqrt{2}}{-8}
=-\frac{\sqrt{2}}{-4}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-4}=\frac{0+2\sqrt{2}}{-8}
=\frac{2\sqrt{2}}{-8}
=\frac{\sqrt{2}}{-4}
$