3x+4/x=7

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 = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*3}=\frac{8}{6}
=1+1/3
$