3+0.5/x=17-3x

Solution for 3+0.5/x=17-3x equation:

3+0.5/x=17-3x

We move all terms to the left:

3+0.5/x-(17-3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

0.5/x+3x-17+3=0

We multiply all the terms by the denominator


3x*x-17*x+3*x+0.5=0

We add all the numbers together, and all the variables

-14x+3x*x+0.5=0

Wy multiply elements

3x^2-14x+0.5=0

a = 3; b = -14; c = +0.5;
Δ = b2-4ac
Δ = -142-4·3·0.5
Δ = 190
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-\sqrt{190}}{2*3}=\frac{14-\sqrt{190}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+\sqrt{190}}{2*3}=\frac{14+\sqrt{190}}{6}
$