13x+17+1/2x-5=180

Solution for 13x+17+1/2x-5=180 equation:

13x+17+1/2x-5=180

We move all terms to the left:

13x+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

13x+1/2x-168=0

We multiply all the terms by the denominator


13x*2x-168*2x+1=0

Wy multiply elements

26x^2-336x+1=0

a = 26; b = -336; c = +1;
Δ = b2-4ac
Δ = -3362-4·26·1
Δ = 112792
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:

$\sqrt{\Delta}=\sqrt{112792}=\sqrt{4*28198}=\sqrt{4}*\sqrt{28198}=2\sqrt{28198}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-2\sqrt{28198}}{2*26}=\frac{336-2\sqrt{28198}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+2\sqrt{28198}}{2*26}=\frac{336+2\sqrt{28198}}{52}
$