1/2x+8x=17

Solution for 1/2x+8x=17 equation:

1/2x+8x=17

We move all terms to the left:

1/2x+8x-(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

8x+1/2x-17=0

We multiply all the terms by the denominator


8x*2x-17*2x+1=0

Wy multiply elements

16x^2-34x+1=0

a = 16; b = -34; c = +1;
Δ = b2-4ac
Δ = -342-4·16·1
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{273}}{2*16}=\frac{34-2\sqrt{273}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{273}}{2*16}=\frac{34+2\sqrt{273}}{32}
$