1/2x-5=8-2x

Solution for 1/2x-5=8-2x equation:

1/2x-5=8-2x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x+2x-8-5=0

We multiply all the terms by the denominator


2x*2x-8*2x-5*2x+1=0

Wy multiply elements

4x^2-16x-10x+1=0

We add all the numbers together, and all the variables

4x^2-26x+1=0

a = 4; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·4·1
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{165}}{2*4}=\frac{26-2\sqrt{165}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{165}}{2*4}=\frac{26+2\sqrt{165}}{8}
$