2x+1/2x+20=90

Solution for 2x+1/2x+20=90 equation:

2x+1/2x+20=90

We move all terms to the left:

2x+1/2x+20-(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

2x+1/2x-70=0

We multiply all the terms by the denominator


2x*2x-70*2x+1=0

Wy multiply elements

4x^2-140x+1=0

a = 4; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·4·1
Δ = 19584
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:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-24\sqrt{34}}{2*4}=\frac{140-24\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+24\sqrt{34}}{2*4}=\frac{140+24\sqrt{34}}{8}
$