4(x2-3)/x=x+2

Solution for 4(x2-3)/x=x+2 equation:

4(x2-3)/x=x+2

We move all terms to the left:

4(x2-3)/x-(x+2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


4(+x^2-3)-x*x-2*x=0

We add all the numbers together, and all the variables

4(+x^2-3)-2x-x*x=0

We multiply parentheses

4x^2-2x-x*x-12=0

Wy multiply elements

4x^2-1x^2-2x-12=0

We add all the numbers together, and all the variables

3x^2-2x-12=0

a = 3; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·3·(-12)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{37}}{2*3}=\frac{2-2\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{37}}{2*3}=\frac{2+2\sqrt{37}}{6}
$