1/2x+2x-9+2x=180

Solution for 1/2x+2x-9+2x=180 equation:

1/2x+2x-9+2x=180

We move all terms to the left:

1/2x+2x-9+2x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x-189=0

We multiply all the terms by the denominator


4x*2x-189*2x+1=0

Wy multiply elements

8x^2-378x+1=0

a = 8; b = -378; c = +1;
Δ = b2-4ac
Δ = -3782-4·8·1
Δ = 142852
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:

$\sqrt{\Delta}=\sqrt{142852}=\sqrt{4*35713}=\sqrt{4}*\sqrt{35713}=2\sqrt{35713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-2\sqrt{35713}}{2*8}=\frac{378-2\sqrt{35713}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+2\sqrt{35713}}{2*8}=\frac{378+2\sqrt{35713}}{16}
$