2/x=3x+4

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

2/x=3x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-3x-4=0

We multiply all the terms by the denominator


-3x*x-4*x+2=0

We add all the numbers together, and all the variables

-4x-3x*x+2=0

Wy multiply elements

-3x^2-4x+2=0

a = -3; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-3)·2
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*-3}=\frac{4-2\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*-3}=\frac{4+2\sqrt{10}}{-6}
$