2x+6+1/2x=90

Solution for 2x+6+1/2x=90 equation:

2x+6+1/2x=90

We move all terms to the left:

2x+6+1/2x-(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-84=0

We multiply all the terms by the denominator


2x*2x-84*2x+1=0

Wy multiply elements

4x^2-168x+1=0

a = 4; b = -168; c = +1;
Δ = b2-4ac
Δ = -1682-4·4·1
Δ = 28208
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:

$\sqrt{\Delta}=\sqrt{28208}=\sqrt{16*1763}=\sqrt{16}*\sqrt{1763}=4\sqrt{1763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1763}}{2*4}=\frac{168-4\sqrt{1763}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1763}}{2*4}=\frac{168+4\sqrt{1763}}{8}
$