(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+5)!=0

x∈R


We get rid of parentheses

3x+1/2x+17+5-180=0

We multiply all the terms by the denominator


3x*2x+17*2x+5*2x-180*2x+1=0

Wy multiply elements

6x^2+34x+10x-360x+1=0

We add all the numbers together, and all the variables

6x^2-316x+1=0

a = 6; b = -316; c = +1;
Δ = b2-4ac
Δ = -3162-4·6·1
Δ = 99832
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:

$\sqrt{\Delta}=\sqrt{99832}=\sqrt{4*24958}=\sqrt{4}*\sqrt{24958}=2\sqrt{24958}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-316)-2\sqrt{24958}}{2*6}=\frac{316-2\sqrt{24958}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-316)+2\sqrt{24958}}{2*6}=\frac{316+2\sqrt{24958}}{12}
$