2/3x+3x+43=180

Solution for 2/3x+3x+43=180 equation:

2/3x+3x+43=180

We move all terms to the left:

2/3x+3x+43-(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+2/3x-137=0

We multiply all the terms by the denominator


3x*3x-137*3x+2=0

Wy multiply elements

9x^2-411x+2=0

a = 9; b = -411; c = +2;
Δ = b2-4ac
Δ = -4112-4·9·2
Δ = 168849
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:

$\sqrt{\Delta}=\sqrt{168849}=\sqrt{9*18761}=\sqrt{9}*\sqrt{18761}=3\sqrt{18761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-411)-3\sqrt{18761}}{2*9}=\frac{411-3\sqrt{18761}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-411)+3\sqrt{18761}}{2*9}=\frac{411+3\sqrt{18761}}{18}
$