3/2x+22x=-26

Solution for 3/2x+22x=-26 equation:

3/2x+22x=-26

We move all terms to the left:

3/2x+22x-(-26)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

22x+3/2x+26=0

We multiply all the terms by the denominator


22x*2x+26*2x+3=0

Wy multiply elements

44x^2+52x+3=0

a = 44; b = 52; c = +3;
Δ = b2-4ac
Δ = 522-4·44·3
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{34}}{2*44}=\frac{-52-8\sqrt{34}}{88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{34}}{2*44}=\frac{-52+8\sqrt{34}}{88}
$