3x-4/x=7

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



3x-4/x=7

We move all terms to the left:

3x-4/x-(7)=0



Domain of the equation: x!=0

x∈R



We multiply all the terms by the denominator


3x*x-7*x-4=0

We add all the numbers together, and all the variables

-7x+3x*x-4=0

Wy multiply elements

3x^2-7x-4=0

a = 3; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·3·(-4)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*3}=\frac{7-\sqrt{97}}{6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*3}=\frac{7+\sqrt{97}}{6}
$

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