1/4a+1/8a+8=22

Solution for 1/4a+1/8a+8=22 equation:

1/4a+1/8a+8=22

We move all terms to the left:

1/4a+1/8a+8-(22)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We add all the numbers together, and all the variables

1/4a+1/8a-14=0

We calculate fractions


8a/32a^2+4a/32a^2-14=0

We multiply all the terms by the denominator


8a+4a-14*32a^2=0

We add all the numbers together, and all the variables

12a-14*32a^2=0

Wy multiply elements

-448a^2+12a=0

a = -448; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-448)·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*-448}=\frac{-24}{-896}
=3/112
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-448}=\frac{0}{-896}
=0
$