3x+17-1/2x-5=180

Solution for 3x+17-1/2x-5=180 equation:

3x+17-1/2x-5=180

We move all terms to the left:

3x+17-1/2x-5-(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

3x-1/2x-168=0

We multiply all the terms by the denominator


3x*2x-168*2x-1=0

Wy multiply elements

6x^2-336x-1=0

a = 6; b = -336; c = -1;
Δ = b2-4ac
Δ = -3362-4·6·(-1)
Δ = 112920
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:

$\sqrt{\Delta}=\sqrt{112920}=\sqrt{4*28230}=\sqrt{4}*\sqrt{28230}=2\sqrt{28230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-2\sqrt{28230}}{2*6}=\frac{336-2\sqrt{28230}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+2\sqrt{28230}}{2*6}=\frac{336+2\sqrt{28230}}{12}
$