a=2(100)/2.483^2

Solution for a=2(100)/2.483^2 equation:

a=2(100)/2.483^2

We move all terms to the left:

a-(2(100)/2.483^2)=0

We get rid of parentheses

a-2100/2.483^2=0

We multiply all the terms by the denominator


a*2.483^2-2100=0

Wy multiply elements

2a^2-2100=0

a = 2; b = 0; c = -2100;
Δ = b2-4ac
Δ = 02-4·2·(-2100)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{42}}{2*2}=\frac{0-20\sqrt{42}}{4}
=-\frac{20\sqrt{42}}{4}
=-5\sqrt{42}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{42}}{2*2}=\frac{0+20\sqrt{42}}{4}
=\frac{20\sqrt{42}}{4}
=5\sqrt{42}
$