(5x)/(x-3)=(8-4)(2x)

Solution for (5x)/(x-3)=(8-4)(2x) equation:

(5x)/(x-3)=(8-4)(2x)

We move all terms to the left:

(5x)/(x-3)-((8-4)(2x))=0


Domain of the equation: (x-3)!=0

We move all terms containing x to the left, all other terms to the right

x!=3

x∈R


We add all the numbers together, and all the variables

5x/(x-3)-(42x)=0

We add all the numbers together, and all the variables

-42x+5x/(x-3)=0

We multiply all the terms by the denominator


-42x*(x-3)+5x=0

We add all the numbers together, and all the variables

5x-42x*(x-3)=0

We multiply parentheses

-42x^2+5x+126x=0

We add all the numbers together, and all the variables

-42x^2+131x=0

a = -42; b = 131; c = 0;
Δ = b2-4ac
Δ = 1312-4·(-42)·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(131)-131}{2*-42}=\frac{-262}{-84}
=3+5/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(131)+131}{2*-42}=\frac{0}{-84}
=0
$