(1/4x)-5=x

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Solution for (1/4x)-5=x equation:



(1/4x)-5=x
We move all terms to the left:
(1/4x)-5-(x)=0
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/4x)-x-5=0
We add all the numbers together, and all the variables
-1x+(+1/4x)-5=0
We get rid of parentheses
-1x+1/4x-5=0
We multiply all the terms by the denominator
-1x*4x-5*4x+1=0
Wy multiply elements
-4x^2-20x+1=0
a = -4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-4)·1
Δ = 416
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:
$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*-4}=\frac{20-4\sqrt{26}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*-4}=\frac{20+4\sqrt{26}}{-8} $

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