9x+1/2x=28

Solution for 9x+1/2x=28 equation:

9x+1/2x=28

We move all terms to the left:

9x+1/2x-(28)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x-28*2x+1=0

Wy multiply elements

18x^2-56x+1=0

a = 18; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·18·1
Δ = 3064
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:

$\sqrt{\Delta}=\sqrt{3064}=\sqrt{4*766}=\sqrt{4}*\sqrt{766}=2\sqrt{766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{766}}{2*18}=\frac{56-2\sqrt{766}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{766}}{2*18}=\frac{56+2\sqrt{766}}{36}
$