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1/4a+1/8a+24=60
We move all terms to the left:
1/4a+1/8a+24-(60)=0
Domain of the equation: 4a!=0
a!=0/4
a!=0
a∈R
Domain of the equation: 8a!=0We add all the numbers together, and all the variables
a!=0/8
a!=0
a∈R
1/4a+1/8a-36=0
We calculate fractions
8a/32a^2+4a/32a^2-36=0
We multiply all the terms by the denominator
8a+4a-36*32a^2=0
We add all the numbers together, and all the variables
12a-36*32a^2=0
Wy multiply elements
-1152a^2+12a=0
a = -1152; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-1152)·0
Δ = 144
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{144}=12$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-1152}=\frac{-24}{-2304} =1/96 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-1152}=\frac{0}{-2304} =0 $
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