1/8a+3/4a=21

Solution for 1/8a+3/4a=21 equation:

1/8a+3/4a=21

We move all terms to the left:

1/8a+3/4a-(21)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We calculate fractions


4a/32a^2+24a/32a^2-21=0

We multiply all the terms by the denominator


4a+24a-21*32a^2=0

We add all the numbers together, and all the variables

28a-21*32a^2=0

Wy multiply elements

-672a^2+28a=0

a = -672; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-672)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-672}=\frac{-56}{-1344}
=1/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-672}=\frac{0}{-1344}
=0
$