5x+1/2x=117

Solution for 5x+1/2x=117 equation:

5x+1/2x=117

We move all terms to the left:

5x+1/2x-(117)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-117*2x+1=0

Wy multiply elements

10x^2-234x+1=0

a = 10; b = -234; c = +1;
Δ = b2-4ac
Δ = -2342-4·10·1
Δ = 54716
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:

$\sqrt{\Delta}=\sqrt{54716}=\sqrt{4*13679}=\sqrt{4}*\sqrt{13679}=2\sqrt{13679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{13679}}{2*10}=\frac{234-2\sqrt{13679}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{13679}}{2*10}=\frac{234+2\sqrt{13679}}{20}
$