1/3x-12x=-24

Solution for 1/3x-12x=-24 equation:

1/3x-12x=-24

We move all terms to the left:

1/3x-12x-(-24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+1/3x+24=0

We multiply all the terms by the denominator


-12x*3x+24*3x+1=0

Wy multiply elements

-36x^2+72x+1=0

a = -36; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-36)·1
Δ = 5328
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:

$\sqrt{\Delta}=\sqrt{5328}=\sqrt{144*37}=\sqrt{144}*\sqrt{37}=12\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{37}}{2*-36}=\frac{-72-12\sqrt{37}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{37}}{2*-36}=\frac{-72+12\sqrt{37}}{-72}
$