5x-1/2x=17

Solution for 5x-1/2x=17 equation:

5x-1/2x=17

We move all terms to the left:

5x-1/2x-(17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-17*2x-1=0

Wy multiply elements

10x^2-34x-1=0

a = 10; b = -34; c = -1;
Δ = b2-4ac
Δ = -342-4·10·(-1)
Δ = 1196
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:

$\sqrt{\Delta}=\sqrt{1196}=\sqrt{4*299}=\sqrt{4}*\sqrt{299}=2\sqrt{299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{299}}{2*10}=\frac{34-2\sqrt{299}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{299}}{2*10}=\frac{34+2\sqrt{299}}{20}
$