1/4(x)+18=x

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Solution for 1/4(x)+18=x equation:



1/4(x)+18=x
We move all terms to the left:
1/4(x)+18-(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
-1x+1/4x+18=0
We multiply all the terms by the denominator
-1x*4x+18*4x+1=0
Wy multiply elements
-4x^2+72x+1=0
a = -4; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-4)·1
Δ = 5200
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:
$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-20\sqrt{13}}{2*-4}=\frac{-72-20\sqrt{13}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+20\sqrt{13}}{2*-4}=\frac{-72+20\sqrt{13}}{-8} $

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