1/4x+1=x-5

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Solution for 1/4x+1=x-5 equation:



1/4x+1=x-5
We move all terms to the left:
1/4x+1-(x-5)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We get rid of parentheses
1/4x-x+5+1=0
We multiply all the terms by the denominator
-x*4x+5*4x+1*4x+1=0
Wy multiply elements
-4x^2+20x+4x+1=0
We add all the numbers together, and all the variables
-4x^2+24x+1=0
a = -4; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-4)·1
Δ = 592
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:
$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{37}}{2*-4}=\frac{-24-4\sqrt{37}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{37}}{2*-4}=\frac{-24+4\sqrt{37}}{-8} $

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