2x+x+1/2x+9=65

Solution for 2x+x+1/2x+9=65 equation:

2x+x+1/2x+9=65

We move all terms to the left:

2x+x+1/2x+9-(65)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-56=0

We multiply all the terms by the denominator


3x*2x-56*2x+1=0

Wy multiply elements

6x^2-112x+1=0

a = 6; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·6·1
Δ = 12520
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:

$\sqrt{\Delta}=\sqrt{12520}=\sqrt{4*3130}=\sqrt{4}*\sqrt{3130}=2\sqrt{3130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-2\sqrt{3130}}{2*6}=\frac{112-2\sqrt{3130}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+2\sqrt{3130}}{2*6}=\frac{112+2\sqrt{3130}}{12}
$