2/3x+5(6x+12)=24

Solution for 2/3x+5(6x+12)=24 equation:

2/3x+5(6x+12)=24

We move all terms to the left:

2/3x+5(6x+12)-(24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

2/3x+30x+60-24=0

We multiply all the terms by the denominator


30x*3x+60*3x-24*3x+2=0

Wy multiply elements

90x^2+180x-72x+2=0

We add all the numbers together, and all the variables

90x^2+108x+2=0

a = 90; b = 108; c = +2;
Δ = b2-4ac
Δ = 1082-4·90·2
Δ = 10944
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:

$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-24\sqrt{19}}{2*90}=\frac{-108-24\sqrt{19}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+24\sqrt{19}}{2*90}=\frac{-108+24\sqrt{19}}{180}
$