3x-11+1/2x=360

Solution for 3x-11+1/2x=360 equation:

3x-11+1/2x=360

We move all terms to the left:

3x-11+1/2x-(360)=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-371=0

We multiply all the terms by the denominator


3x*2x-371*2x+1=0

Wy multiply elements

6x^2-742x+1=0

a = 6; b = -742; c = +1;
Δ = b2-4ac
Δ = -7422-4·6·1
Δ = 550540
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:

$\sqrt{\Delta}=\sqrt{550540}=\sqrt{4*137635}=\sqrt{4}*\sqrt{137635}=2\sqrt{137635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-742)-2\sqrt{137635}}{2*6}=\frac{742-2\sqrt{137635}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-742)+2\sqrt{137635}}{2*6}=\frac{742+2\sqrt{137635}}{12}
$