a+3/2a+2a+6a=1400

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Solution for a+3/2a+2a+6a=1400 equation: 



a+3/2a+2a+6a=1400

We move all terms to the left:

a+3/2a+2a+6a-(1400)=0



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



We add all the numbers together, and all the variables

9a+3/2a-1400=0

We multiply all the terms by the denominator


9a*2a-1400*2a+3=0

Wy multiply elements

18a^2-2800a+3=0

a = 18; b = -2800; c = +3;
Δ = b2-4ac
Δ = -28002-4·18·3
Δ = 7839784
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:


$\sqrt{\Delta}=\sqrt{7839784}=\sqrt{4*1959946}=\sqrt{4}*\sqrt{1959946}=2\sqrt{1959946}$


$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2800)-2\sqrt{1959946}}{2*18}=\frac{2800-2\sqrt{1959946}}{36}
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2800)+2\sqrt{1959946}}{2*18}=\frac{2800+2\sqrt{1959946}}{36}
$

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