(2/3)*a=27/8

Solution for (2/3)*a=27/8 equation:

(2/3)*a=27/8

We move all terms to the left:

(2/3)*a-(27/8)=0


Domain of the equation: 3)*a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+2/3)*a-(+27/8)=0

We multiply parentheses

2a^2-(+27/8)=0

We get rid of parentheses

2a^2-27/8=0

We multiply all the terms by the denominator


2a^2*8-27=0

Wy multiply elements

16a^2-27=0

a = 16; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·16·(-27)
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*16}=\frac{0-24\sqrt{3}}{32}
=-\frac{24\sqrt{3}}{32}
=-\frac{3\sqrt{3}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*16}=\frac{0+24\sqrt{3}}{32}
=\frac{24\sqrt{3}}{32}
=\frac{3\sqrt{3}}{4}
$