1/3x+24=-2x+6

Solution for 1/3x+24=-2x+6 equation:

1/3x+24=-2x+6

We move all terms to the left:

1/3x+24-(-2x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+2x-6+24=0

We multiply all the terms by the denominator


2x*3x-6*3x+24*3x+1=0

Wy multiply elements

6x^2-18x+72x+1=0

We add all the numbers together, and all the variables

6x^2+54x+1=0

a = 6; b = 54; c = +1;
Δ = b2-4ac
Δ = 542-4·6·1
Δ = 2892
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:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{723}}{2*6}=\frac{-54-2\sqrt{723}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{723}}{2*6}=\frac{-54+2\sqrt{723}}{12}
$