3/2x=x+17

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

3/2x=x+17

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-x-17=0

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2-34x+3=0

a = -2; b = -34; c = +3;
Δ = b2-4ac
Δ = -342-4·(-2)·3
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{295}}{2*-2}=\frac{34-2\sqrt{295}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{295}}{2*-2}=\frac{34+2\sqrt{295}}{-4}
$