4x+1/2x=2+17

Solution for 4x+1/2x=2+17 equation:

4x+1/2x=2+17

We move all terms to the left:

4x+1/2x-(2+17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x-19=0

We multiply all the terms by the denominator


4x*2x-19*2x+1=0

Wy multiply elements

8x^2-38x+1=0

a = 8; b = -38; c = +1;
Δ = b2-4ac
Δ = -382-4·8·1
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{353}}{2*8}=\frac{38-2\sqrt{353}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{353}}{2*8}=\frac{38+2\sqrt{353}}{16}
$