2(4a+8)=3(8/3a-10)

Solution for 2(4a+8)=3(8/3a-10) equation:

2(4a+8)=3(8/3a-10)

We move all terms to the left:

2(4a+8)-(3(8/3a-10))=0


Domain of the equation: 3a-10))!=0

a∈R


We multiply parentheses

8a-(3(8/3a-10))+16=0

We multiply all the terms by the denominator


8a*3a+16*3a-10))-(3(8-10))=0

We add all the numbers together, and all the variables

8a*3a+16*3a-10))-(3(-2))=0

We add all the numbers together, and all the variables

8a*3a+16*3a=0

Wy multiply elements

24a^2+48a=0

a = 24; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·24·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*24}=\frac{-96}{48}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*24}=\frac{0}{48}
=0
$