a=2(478)/1.63^2

Solution for a=2(478)/1.63^2 equation:

a=2(478)/1.63^2

We move all terms to the left:

a-(2(478)/1.63^2)=0

We get rid of parentheses

a-2478/1.63^2=0

We multiply all the terms by the denominator


a*1.63^2-2478=0

Wy multiply elements

a^2-2478=0

a = 1; b = 0; c = -2478;
Δ = b2-4ac
Δ = 02-4·1·(-2478)
Δ = 9912
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:

$\sqrt{\Delta}=\sqrt{9912}=\sqrt{4*2478}=\sqrt{4}*\sqrt{2478}=2\sqrt{2478}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2478}}{2*1}=\frac{0-2\sqrt{2478}}{2}
=-\frac{2\sqrt{2478}}{2}
=-\sqrt{2478}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2478}}{2*1}=\frac{0+2\sqrt{2478}}{2}
=\frac{2\sqrt{2478}}{2}
=\sqrt{2478}
$