x+3/4x=14

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Solution for x+3/4x=14 equation:



x+3/4x=14
We move all terms to the left:
x+3/4x-(14)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We multiply all the terms by the denominator
x*4x-14*4x+3=0
Wy multiply elements
4x^2-56x+3=0
a = 4; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·4·3
Δ = 3088
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:
$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{193}}{2*4}=\frac{56-4\sqrt{193}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{193}}{2*4}=\frac{56+4\sqrt{193}}{8} $

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