6x+1/2x=14

Solution for 6x+1/2x=14 equation:

6x+1/2x=14

We move all terms to the left:

6x+1/2x-(14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


6x*2x-14*2x+1=0

Wy multiply elements

12x^2-28x+1=0

a = 12; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·12·1
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{46}}{2*12}=\frac{28-4\sqrt{46}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{46}}{2*12}=\frac{28+4\sqrt{46}}{24}
$