1/3x+24=3x-12

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

1/3x+24=3x-12

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+36x+72x+1=0

We add all the numbers together, and all the variables

-9x^2+108x+1=0

a = -9; b = 108; c = +1;
Δ = b2-4ac
Δ = 1082-4·(-9)·1
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-30\sqrt{13}}{2*-9}=\frac{-108-30\sqrt{13}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+30\sqrt{13}}{2*-9}=\frac{-108+30\sqrt{13}}{-18}
$