(2/3)a+1=16-a

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Solution for (2/3)a+1=16-a equation:



(2/3)a+1=16-a
We move all terms to the left:
(2/3)a+1-(16-a)=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-(-1a+16)+1=0
We multiply parentheses
2a^2-(-1a+16)+1=0
We get rid of parentheses
2a^2+1a-16+1=0
We add all the numbers together, and all the variables
2a^2+a-15=0
a = 2; b = 1; c = -15;
Δ = b2-4ac
Δ = 12-4·2·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*2}=\frac{-12}{4} =-3 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*2}=\frac{10}{4} =2+1/2 $

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