5/8a+1/2a=20

Solution for 5/8a+1/2a=20 equation:

5/8a+1/2a=20

We move all terms to the left:

5/8a+1/2a-(20)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We calculate fractions


10a/16a^2+8a/16a^2-20=0

We multiply all the terms by the denominator


10a+8a-20*16a^2=0

We add all the numbers together, and all the variables

18a-20*16a^2=0

Wy multiply elements

-320a^2+18a=0

a = -320; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-320)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-320}=\frac{-36}{-640}
=9/160
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-320}=\frac{0}{-640}
=0
$