72=2/3x+2x

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

72=2/3x+2x

We move all terms to the left:

72-(2/3x+2x)=0


Domain of the equation: 3x+2x)!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+2/3x)+72=0

We get rid of parentheses

-2x-2/3x+72=0

We multiply all the terms by the denominator


-2x*3x+72*3x-2=0

Wy multiply elements

-6x^2+216x-2=0

a = -6; b = 216; c = -2;
Δ = b2-4ac
Δ = 2162-4·(-6)·(-2)
Δ = 46608
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:

$\sqrt{\Delta}=\sqrt{46608}=\sqrt{16*2913}=\sqrt{16}*\sqrt{2913}=4\sqrt{2913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-4\sqrt{2913}}{2*-6}=\frac{-216-4\sqrt{2913}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+4\sqrt{2913}}{2*-6}=\frac{-216+4\sqrt{2913}}{-12}
$