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

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

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

We move all terms to the left:

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

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-182x+8=0

a = 4; b = -182; c = +8;
Δ = b2-4ac
Δ = -1822-4·4·8
Δ = 32996
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:

$\sqrt{\Delta}=\sqrt{32996}=\sqrt{4*8249}=\sqrt{4}*\sqrt{8249}=2\sqrt{8249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-2\sqrt{8249}}{2*4}=\frac{182-2\sqrt{8249}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+2\sqrt{8249}}{2*4}=\frac{182+2\sqrt{8249}}{8}
$