14a+1/3a+8=22

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Solution for 14a+1/3a+8=22 equation:



14a+1/3a+8=22
We move all terms to the left:
14a+1/3a+8-(22)=0
Domain of the equation: 3a!=0
a!=0/3
a!=0
a∈R
We add all the numbers together, and all the variables
14a+1/3a-14=0
We multiply all the terms by the denominator
14a*3a-14*3a+1=0
Wy multiply elements
42a^2-42a+1=0
a = 42; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·42·1
Δ = 1596
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:
$\sqrt{\Delta}=\sqrt{1596}=\sqrt{4*399}=\sqrt{4}*\sqrt{399}=2\sqrt{399}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{399}}{2*42}=\frac{42-2\sqrt{399}}{84} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{399}}{2*42}=\frac{42+2\sqrt{399}}{84} $

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