x+44+2x+28+1/4x+56=180

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Solution for x+44+2x+28+1/4x+56=180 equation:



x+44+2x+28+1/4x+56=180
We move all terms to the left:
x+44+2x+28+1/4x+56-(180)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
3x+1/4x-52=0
We multiply all the terms by the denominator
3x*4x-52*4x+1=0
Wy multiply elements
12x^2-208x+1=0
a = 12; b = -208; c = +1;
Δ = b2-4ac
Δ = -2082-4·12·1
Δ = 43216
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:
$\sqrt{\Delta}=\sqrt{43216}=\sqrt{16*2701}=\sqrt{16}*\sqrt{2701}=4\sqrt{2701}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-4\sqrt{2701}}{2*12}=\frac{208-4\sqrt{2701}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+4\sqrt{2701}}{2*12}=\frac{208+4\sqrt{2701}}{24} $

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