x=1-(3x^2)/(x-4)

Solution for x=1-(3x^2)/(x-4) equation:

x=1-(3x^2)/(x-4)

We move all terms to the left:

x-(1-(3x^2)/(x-4))=0


Domain of the equation: (x-4))!=0

x∈R


determiningTheFunctionDomain
-(1-3x^2/(x-4))+x=0

We multiply all the terms by the denominator


-(1-3x^2+x*(x-4))=0


We calculate terms in parentheses: -(1-3x^2+x*(x-4)), so:

1-3x^2+x*(x-4)

determiningTheFunctionDomain
-3x^2+x*(x-4)+1

We multiply parentheses

-3x^2+x^2-4x+1

We add all the numbers together, and all the variables

-2x^2-4x+1

Back to the equation:

-(-2x^2-4x+1)


We get rid of parentheses

2x^2+4x-1=0

a = 2; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·2·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*2}=\frac{-4-2\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*2}=\frac{-4+2\sqrt{6}}{4}
$