3/2x+2x=36

Solution for 3/2x+2x=36 equation:

3/2x+2x=36

We move all terms to the left:

3/2x+2x-(36)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/2x-36=0

We multiply all the terms by the denominator


2x*2x-36*2x+3=0

Wy multiply elements

4x^2-72x+3=0

a = 4; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·4·3
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{321}}{2*4}=\frac{72-4\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{321}}{2*4}=\frac{72+4\sqrt{321}}{8}
$