3x+1/2x=17-3x

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

3x+1/2x=17-3x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

12x^2-34x+1=0

a = 12; b = -34; c = +1;
Δ = b2-4ac
Δ = -342-4·12·1
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{277}}{2*12}=\frac{34-2\sqrt{277}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{277}}{2*12}=\frac{34+2\sqrt{277}}{24}
$