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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x*2x+17*2x-5))-((-4))=0

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2+34x=0

a = 6; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·6·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*6}=\frac{-68}{12}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*6}=\frac{0}{12}
=0
$