x+2/3x+50=180

Solution for x+2/3x+50=180 equation:

x+2/3x+50=180

We move all terms to the left:

x+2/3x+50-(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

x+2/3x-130=0

We multiply all the terms by the denominator


x*3x-130*3x+2=0

Wy multiply elements

3x^2-390x+2=0

a = 3; b = -390; c = +2;
Δ = b2-4ac
Δ = -3902-4·3·2
Δ = 152076
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:

$\sqrt{\Delta}=\sqrt{152076}=\sqrt{4*38019}=\sqrt{4}*\sqrt{38019}=2\sqrt{38019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-390)-2\sqrt{38019}}{2*3}=\frac{390-2\sqrt{38019}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-390)+2\sqrt{38019}}{2*3}=\frac{390+2\sqrt{38019}}{6}
$