X+2/3x+72=216

Solution for X+2/3x+72=216 equation:

X+2/3X+72=216

We move all terms to the left:

X+2/3X+72-(216)=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+2/3X-144=0

We multiply all the terms by the denominator


X*3X-144*3X+2=0

Wy multiply elements

3X^2-432X+2=0

a = 3; b = -432; c = +2;
Δ = b2-4ac
Δ = -4322-4·3·2
Δ = 186600
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:

$\sqrt{\Delta}=\sqrt{186600}=\sqrt{100*1866}=\sqrt{100}*\sqrt{1866}=10\sqrt{1866}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-10\sqrt{1866}}{2*3}=\frac{432-10\sqrt{1866}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+10\sqrt{1866}}{2*3}=\frac{432+10\sqrt{1866}}{6}
$