(3x-17)+(1/2x-5)=360

Solution for (3x-17)+(1/2x-5)=360 equation:

(3x-17)+(1/2x-5)=360

We move all terms to the left:

(3x-17)+(1/2x-5)-(360)=0


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

3x+1/2x-17-5-360=0

We multiply all the terms by the denominator


3x*2x-17*2x-5*2x-360*2x+1=0

Wy multiply elements

6x^2-34x-10x-720x+1=0

We add all the numbers together, and all the variables

6x^2-764x+1=0

a = 6; b = -764; c = +1;
Δ = b2-4ac
Δ = -7642-4·6·1
Δ = 583672
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:

$\sqrt{\Delta}=\sqrt{583672}=\sqrt{4*145918}=\sqrt{4}*\sqrt{145918}=2\sqrt{145918}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-764)-2\sqrt{145918}}{2*6}=\frac{764-2\sqrt{145918}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-764)+2\sqrt{145918}}{2*6}=\frac{764+2\sqrt{145918}}{12}
$