(1/3)x+6=(81)-x

Solution for (1/3)x+6=(81)-x equation:

(1/3)x+6=(81)-x

We move all terms to the left:

(1/3)x+6-((81)-x)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)x-(-1x+81)+6=0

We multiply parentheses

x^2-(-1x+81)+6=0

We get rid of parentheses

x^2+1x-81+6=0

We add all the numbers together, and all the variables

x^2+x-75=0

a = 1; b = 1; c = -75;
Δ = b2-4ac
Δ = 12-4·1·(-75)
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{301}}{2*1}=\frac{-1-\sqrt{301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{301}}{2*1}=\frac{-1+\sqrt{301}}{2}
$