3/2x+x+2x+3x=90

Solution for 3/2x+x+2x+3x=90 equation:

3/2x+x+2x+3x=90

We move all terms to the left:

3/2x+x+2x+3x-(90)=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-90=0

We multiply all the terms by the denominator


6x*2x-90*2x+3=0

Wy multiply elements

12x^2-180x+3=0

a = 12; b = -180; c = +3;
Δ = b2-4ac
Δ = -1802-4·12·3
Δ = 32256
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:

$\sqrt{\Delta}=\sqrt{32256}=\sqrt{2304*14}=\sqrt{2304}*\sqrt{14}=48\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-48\sqrt{14}}{2*12}=\frac{180-48\sqrt{14}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+48\sqrt{14}}{2*12}=\frac{180+48\sqrt{14}}{24}
$