(1/4)a-3=1024

Solution for (1/4)a-3=1024 equation:

(1/4)a-3=1024

We move all terms to the left:

(1/4)a-3-(1024)=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-3-1024=0

We add all the numbers together, and all the variables

(+1/4)a-1027=0

We multiply parentheses

a^2-1027=0

a = 1; b = 0; c = -1027;
Δ = b2-4ac
Δ = 02-4·1·(-1027)
Δ = 4108
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:

$\sqrt{\Delta}=\sqrt{4108}=\sqrt{4*1027}=\sqrt{4}*\sqrt{1027}=2\sqrt{1027}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1027}}{2*1}=\frac{0-2\sqrt{1027}}{2}
=-\frac{2\sqrt{1027}}{2}
=-\sqrt{1027}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1027}}{2*1}=\frac{0+2\sqrt{1027}}{2}
=\frac{2\sqrt{1027}}{2}
=\sqrt{1027}
$