X/3x-20+x=180

Solution for X/3x-20+x=180 equation:

X/3X-20+X=180

We move all terms to the left:

X/3X-20+X-(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+X/3X-200=0

We multiply all the terms by the denominator


X*3X+X-200*3X=0

We add all the numbers together, and all the variables

X+X*3X-200*3X=0

Wy multiply elements

3X^2+X-600X=0

We add all the numbers together, and all the variables

3X^2-599X=0

a = 3; b = -599; c = 0;
Δ = b2-4ac
Δ = -5992-4·3·0
Δ = 358801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{358801}=599$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-599)-599}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-599)+599}{2*3}=\frac{1198}{6}
=199+2/3
$