(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+17)+1/2x=0

We get rid of parentheses

3x+1/2x+17=0

We multiply all the terms by the denominator


3x*2x+17*2x+1=0

Wy multiply elements

6x^2+34x+1=0

a = 6; b = 34; c = +1;
Δ = b2-4ac
Δ = 342-4·6·1
Δ = 1132
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:

$\sqrt{\Delta}=\sqrt{1132}=\sqrt{4*283}=\sqrt{4}*\sqrt{283}=2\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{283}}{2*6}=\frac{-34-2\sqrt{283}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{283}}{2*6}=\frac{-34+2\sqrt{283}}{12}
$