3+(1/4)a=33

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Solution for 3+(1/4)a=33 equation:



3+(1/4)a=33
We move all terms to the left:
3+(1/4)a-(33)=0
Domain of the equation: 4)a!=0
a!=0/1
a!=0
a∈R
We add all the numbers together, and all the variables
(+1/4)a+3-33=0
We add all the numbers together, and all the variables
(+1/4)a-30=0
We multiply parentheses
a^2-30=0
a = 1; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·1·(-30)
Δ = 120
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:
$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*1}=\frac{0-2\sqrt{30}}{2} =-\frac{2\sqrt{30}}{2} =-\sqrt{30} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*1}=\frac{0+2\sqrt{30}}{2} =\frac{2\sqrt{30}}{2} =\sqrt{30} $

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