2x+4/3x+20=180

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Solution for 2x+4/3x+20=180 equation: 



2x+4/3x+20=180

We move all terms to the left:

2x+4/3x+20-(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

2x+4/3x-160=0

We multiply all the terms by the denominator


2x*3x-160*3x+4=0

Wy multiply elements

6x^2-480x+4=0

a = 6; b = -480; c = +4;
Δ = b2-4ac
Δ = -4802-4·6·4
Δ = 230304
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:


$\sqrt{\Delta}=\sqrt{230304}=\sqrt{16*14394}=\sqrt{16}*\sqrt{14394}=4\sqrt{14394}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-4\sqrt{14394}}{2*6}=\frac{480-4\sqrt{14394}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+4\sqrt{14394}}{2*6}=\frac{480+4\sqrt{14394}}{12}
$

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