x+2X+1/3(2x)=121

Solution for x+2X+1/3(2x)=121 equation:

x+2x+1/3(2x)=121

We move all terms to the left:

x+2x+1/3(2x)-(121)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/32x-121=0

We multiply all the terms by the denominator


3x*32x-121*32x+1=0

Wy multiply elements

96x^2-3872x+1=0

a = 96; b = -3872; c = +1;
Δ = b2-4ac
Δ = -38722-4·96·1
Δ = 14992000
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:

$\sqrt{\Delta}=\sqrt{14992000}=\sqrt{1600*9370}=\sqrt{1600}*\sqrt{9370}=40\sqrt{9370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3872)-40\sqrt{9370}}{2*96}=\frac{3872-40\sqrt{9370}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3872)+40\sqrt{9370}}{2*96}=\frac{3872+40\sqrt{9370}}{192}
$