36/x=24-3x

Solution for 36/x=24-3x equation:

36/x=24-3x

We move all terms to the left:

36/x-(24-3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

36/x-(-3x+24)=0

We get rid of parentheses

36/x+3x-24=0

We multiply all the terms by the denominator


3x*x-24*x+36=0

We add all the numbers together, and all the variables

-24x+3x*x+36=0

Wy multiply elements

3x^2-24x+36=0

a = 3; b = -24; c = +36;
Δ = b2-4ac
Δ = -242-4·3·36
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*3}=\frac{12}{6}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*3}=\frac{36}{6}
=6
$