3/2x+x+2x+3x=270

Solution for 3/2x+x+2x+3x=270 equation:

3/2x+x+2x+3x=270

We move all terms to the left:

3/2x+x+2x+3x-(270)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6x+3/2x-270=0

We multiply all the terms by the denominator


6x*2x-270*2x+3=0

Wy multiply elements

12x^2-540x+3=0

a = 12; b = -540; c = +3;
Δ = b2-4ac
Δ = -5402-4·12·3
Δ = 291456
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:

$\sqrt{\Delta}=\sqrt{291456}=\sqrt{576*506}=\sqrt{576}*\sqrt{506}=24\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-24\sqrt{506}}{2*12}=\frac{540-24\sqrt{506}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+24\sqrt{506}}{2*12}=\frac{540+24\sqrt{506}}{24}
$