x+3/2x+x+2x-45=540

Solution for x+3/2x+x+2x-45=540 equation:

x+3/2x+x+2x-45=540

We move all terms to the left:

x+3/2x+x+2x-45-(540)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/2x-585=0

We multiply all the terms by the denominator


4x*2x-585*2x+3=0

Wy multiply elements

8x^2-1170x+3=0

a = 8; b = -1170; c = +3;
Δ = b2-4ac
Δ = -11702-4·8·3
Δ = 1368804
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:

$\sqrt{\Delta}=\sqrt{1368804}=\sqrt{4*342201}=\sqrt{4}*\sqrt{342201}=2\sqrt{342201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1170)-2\sqrt{342201}}{2*8}=\frac{1170-2\sqrt{342201}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1170)+2\sqrt{342201}}{2*8}=\frac{1170+2\sqrt{342201}}{16}
$