8/4x+5=23-x

Solution for 8/4x+5=23-x equation:

8/4x+5=23-x

We move all terms to the left:

8/4x+5-(23-x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8/4x-(-1x+23)+5=0

We get rid of parentheses

8/4x+1x-23+5=0

We multiply all the terms by the denominator


1x*4x-23*4x+5*4x+8=0

Wy multiply elements

4x^2-92x+20x+8=0

We add all the numbers together, and all the variables

4x^2-72x+8=0

a = 4; b = -72; c = +8;
Δ = b2-4ac
Δ = -722-4·4·8
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{79}}{2*4}=\frac{72-8\sqrt{79}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{79}}{2*4}=\frac{72+8\sqrt{79}}{8}
$