(2/3)a-8=11

Solution for (2/3)a-8=11 equation:

(2/3)a-8=11

We move all terms to the left:

(2/3)a-8-(11)=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-8-11=0

We add all the numbers together, and all the variables

(+2/3)a-19=0

We multiply parentheses

2a^2-19=0

a = 2; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·2·(-19)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{38}}{2*2}=\frac{0-2\sqrt{38}}{4}
=-\frac{2\sqrt{38}}{4}
=-\frac{\sqrt{38}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{38}}{2*2}=\frac{0+2\sqrt{38}}{4}
=\frac{2\sqrt{38}}{4}
=\frac{\sqrt{38}}{2}
$