6-(3-x)=217/2x

Solution for 6-(3-x)=217/2x equation:

6-(3-x)=217/2x

We move all terms to the left:

6-(3-x)-(217/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+3)-(+217/2x)+6=0

We get rid of parentheses

1x-217/2x-3+6=0

We multiply all the terms by the denominator


1x*2x-3*2x+6*2x-217=0

Wy multiply elements

2x^2-6x+12x-217=0

We add all the numbers together, and all the variables

2x^2+6x-217=0

a = 2; b = 6; c = -217;
Δ = b2-4ac
Δ = 62-4·2·(-217)
Δ = 1772
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:

$\sqrt{\Delta}=\sqrt{1772}=\sqrt{4*443}=\sqrt{4}*\sqrt{443}=2\sqrt{443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{443}}{2*2}=\frac{-6-2\sqrt{443}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{443}}{2*2}=\frac{-6+2\sqrt{443}}{4}
$