7x-3/(4x)=3

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Solution for 7x-3/(4x)=3 equation:



7x-3/(4x)=3
We move all terms to the left:
7x-3/(4x)-(3)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We multiply all the terms by the denominator
7x*4x-3*4x-3=0
Wy multiply elements
28x^2-12x-3=0
a = 28; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·28·(-3)
Δ = 480
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:
$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{30}}{2*28}=\frac{12-4\sqrt{30}}{56} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{30}}{2*28}=\frac{12+4\sqrt{30}}{56} $

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