4x=27/x+3

Solution for 4x=27/x+3 equation:

4x=27/x+3

We move all terms to the left:

4x-(27/x+3)=0


Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

4x-27/x-3=0

We multiply all the terms by the denominator


4x*x-3*x-27=0

We add all the numbers together, and all the variables

-3x+4x*x-27=0

Wy multiply elements

4x^2-3x-27=0

a = 4; b = -3; c = -27;
Δ = b2-4ac
Δ = -32-4·4·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*4}=\frac{-18}{8}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*4}=\frac{24}{8}
=3
$