2x-4/x+7=3

Solution for 2x-4/x+7=3 equation:

2x-4/x+7=3

We move all terms to the left:

2x-4/x+7-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-4/x+4=0

We multiply all the terms by the denominator


2x*x+4*x-4=0

We add all the numbers together, and all the variables

4x+2x*x-4=0

Wy multiply elements

2x^2+4x-4=0

a = 2; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·2·(-4)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*2}=\frac{-4-4\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*2}=\frac{-4+4\sqrt{3}}{4}
$