x+3x+1/4x=7225

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Solution for x+3x+1/4x=7225 equation:



x+3x+1/4x=7225
We move all terms to the left:
x+3x+1/4x-(7225)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
4x+1/4x-7225=0
We multiply all the terms by the denominator
4x*4x-7225*4x+1=0
Wy multiply elements
16x^2-28900x+1=0
a = 16; b = -28900; c = +1;
Δ = b2-4ac
Δ = -289002-4·16·1
Δ = 835209936
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:
$\sqrt{\Delta}=\sqrt{835209936}=\sqrt{144*5800069}=\sqrt{144}*\sqrt{5800069}=12\sqrt{5800069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28900)-12\sqrt{5800069}}{2*16}=\frac{28900-12\sqrt{5800069}}{32} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28900)+12\sqrt{5800069}}{2*16}=\frac{28900+12\sqrt{5800069}}{32} $

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