a+3/4(a)=21

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Solution for a+3/4(a)=21 equation:



a+3/4(a)=21
We move all terms to the left:
a+3/4(a)-(21)=0
Domain of the equation: 4a!=0
a!=0/4
a!=0
a∈R
We multiply all the terms by the denominator
a*4a-21*4a+3=0
Wy multiply elements
4a^2-84a+3=0
a = 4; b = -84; c = +3;
Δ = b2-4ac
Δ = -842-4·4·3
Δ = 7008
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:
$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{438}}{2*4}=\frac{84-4\sqrt{438}}{8} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{438}}{2*4}=\frac{84+4\sqrt{438}}{8} $

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