x-3-1/4x=x+12-1x

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Solution for x-3-1/4x=x+12-1x equation:



x-3-1/4x=x+12-1x
We move all terms to the left:
x-3-1/4x-(x+12-1x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
x-1/4x-3-12=0
We add all the numbers together, and all the variables
x-1/4x-15=0
We multiply all the terms by the denominator
x*4x-15*4x-1=0
Wy multiply elements
4x^2-60x-1=0
a = 4; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·4·(-1)
Δ = 3616
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:
$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*4}=\frac{60-4\sqrt{226}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*4}=\frac{60+4\sqrt{226}}{8} $

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