X-180=2/3x

Solution for X-180=2/3x equation:

X-180=2/3X

We move all terms to the left:

X-180-(2/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+2/3X)-180=0

We get rid of parentheses

X-2/3X-180=0

We multiply all the terms by the denominator


X*3X-180*3X-2=0

Wy multiply elements

3X^2-540X-2=0

a = 3; b = -540; c = -2;
Δ = b2-4ac
Δ = -5402-4·3·(-2)
Δ = 291624
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:

$\sqrt{\Delta}=\sqrt{291624}=\sqrt{4*72906}=\sqrt{4}*\sqrt{72906}=2\sqrt{72906}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72906}}{2*3}=\frac{540-2\sqrt{72906}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72906}}{2*3}=\frac{540+2\sqrt{72906}}{6}
$