X=(1/3)(180-x)

Solution for X=(1/3)(180-x) equation:

X=(1/3)(180-X)

We move all terms to the left:

X-((1/3)(180-X))=0


Domain of the equation: 3)(180-X))!=0

X∈R


We add all the numbers together, and all the variables

X-((+1/3)(-1X+180))=0

We multiply parentheses ..

-((-1X^2+1/3*180))+X=0

We multiply all the terms by the denominator


-((-1X^2+1+X*3*180))=0


We calculate terms in parentheses: -((-1X^2+1+X*3*180)), so:

(-1X^2+1+X*3*180)

We get rid of parentheses

-1X^2+X*3*180+1

Wy multiply elements

-1X^2+540X*1+1

Wy multiply elements

-1X^2+540X+1

Back to the equation:

-(-1X^2+540X+1)


We get rid of parentheses

1X^2-540X-1=0

We add all the numbers together, and all the variables

X^2-540X-1=0

a = 1; b = -540; c = -1;
Δ = b2-4ac
Δ = -5402-4·1·(-1)
Δ = 291604
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:

$\sqrt{\Delta}=\sqrt{291604}=\sqrt{4*72901}=\sqrt{4}*\sqrt{72901}=2\sqrt{72901}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72901}}{2*1}=\frac{540-2\sqrt{72901}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72901}}{2*1}=\frac{540+2\sqrt{72901}}{2}
$