X=60+2/3x

Solution for X=60+2/3x equation:

X=60+2/3X

We move all terms to the left:

X-(60+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+60)=0

We get rid of parentheses

X-2/3X-60=0

We multiply all the terms by the denominator


X*3X-60*3X-2=0

Wy multiply elements

3X^2-180X-2=0

a = 3; b = -180; c = -2;
Δ = b2-4ac
Δ = -1802-4·3·(-2)
Δ = 32424
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:

$\sqrt{\Delta}=\sqrt{32424}=\sqrt{4*8106}=\sqrt{4}*\sqrt{8106}=2\sqrt{8106}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8106}}{2*3}=\frac{180-2\sqrt{8106}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8106}}{2*3}=\frac{180+2\sqrt{8106}}{6}
$