a=96/2.05^2

Solution for a=96/2.05^2 equation:

a=96/2.05^2

We move all terms to the left:

a-(96/2.05^2)=0

We get rid of parentheses

a-96/2.05^2=0

We multiply all the terms by the denominator


a*2.05^2-96=0

Wy multiply elements

2a^2-96=0

a = 2; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·2·(-96)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*2}=\frac{0-16\sqrt{3}}{4}
=-\frac{16\sqrt{3}}{4}
=-4\sqrt{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*2}=\frac{0+16\sqrt{3}}{4}
=\frac{16\sqrt{3}}{4}
=4\sqrt{3}
$