4x+1/2x=13

Solution for 4x+1/2x=13 equation:

4x+1/2x=13

We move all terms to the left:

4x+1/2x-(13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-13*2x+1=0

Wy multiply elements

8x^2-26x+1=0

a = 8; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·8·1
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{161}}{2*8}=\frac{26-2\sqrt{161}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{161}}{2*8}=\frac{26+2\sqrt{161}}{16}
$