x+3/2x+2x+5/2x=91

Solution for x+3/2x+2x+5/2x=91 equation:

x+3/2x+2x+5/2x=91

We move all terms to the left:

x+3/2x+2x+5/2x-(91)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+3/2x+5/2x-91=0

We multiply all the terms by the denominator


3x*2x-91*2x+3+5=0

We add all the numbers together, and all the variables

3x*2x-91*2x+8=0

Wy multiply elements

6x^2-182x+8=0

a = 6; b = -182; c = +8;
Δ = b2-4ac
Δ = -1822-4·6·8
Δ = 32932
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:

$\sqrt{\Delta}=\sqrt{32932}=\sqrt{4*8233}=\sqrt{4}*\sqrt{8233}=2\sqrt{8233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-2\sqrt{8233}}{2*6}=\frac{182-2\sqrt{8233}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+2\sqrt{8233}}{2*6}=\frac{182+2\sqrt{8233}}{12}
$