x+8=5/2x+8

Solution for x+8=5/2x+8 equation:

x+8=5/2x+8

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-16x+16x-5=0

We add all the numbers together, and all the variables

2x^2-5=0

a = 2; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·2·(-5)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*2}=\frac{0-2\sqrt{10}}{4}
=-\frac{2\sqrt{10}}{4}
=-\frac{\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*2}=\frac{0+2\sqrt{10}}{4}
=\frac{2\sqrt{10}}{4}
=\frac{\sqrt{10}}{2}
$