2/3x+16=6x+24

Solution for 2/3x+16=6x+24 equation:

2/3x+16=6x+24

We move all terms to the left:

2/3x+16-(6x+24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-6x-24+16=0

We multiply all the terms by the denominator


-6x*3x-24*3x+16*3x+2=0

Wy multiply elements

-18x^2-72x+48x+2=0

We add all the numbers together, and all the variables

-18x^2-24x+2=0

a = -18; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-18)·2
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*-18}=\frac{24-12\sqrt{5}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*-18}=\frac{24+12\sqrt{5}}{-36}
$