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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2+44x-1=0

a = 6; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·6·(-1)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-14\sqrt{10}}{2*6}=\frac{-44-14\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+14\sqrt{10}}{2*6}=\frac{-44+14\sqrt{10}}{12}
$