3x+24+4/3x=180

Solution for 3x+24+4/3x=180 equation:

3x+24+4/3x=180

We move all terms to the left:

3x+24+4/3x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/3x-156=0

We multiply all the terms by the denominator


3x*3x-156*3x+4=0

Wy multiply elements

9x^2-468x+4=0

a = 9; b = -468; c = +4;
Δ = b2-4ac
Δ = -4682-4·9·4
Δ = 218880
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:

$\sqrt{\Delta}=\sqrt{218880}=\sqrt{2304*95}=\sqrt{2304}*\sqrt{95}=48\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-48\sqrt{95}}{2*9}=\frac{468-48\sqrt{95}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+48\sqrt{95}}{2*9}=\frac{468+48\sqrt{95}}{18}
$