8/4x+5=23-x

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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} $

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