5a^2=42^2+4

Solution for 5a^2=42^2+4 equation:

5a^2=42^2+4

We move all terms to the left:

5a^2-(42^2+4)=0

We add all the numbers together, and all the variables

5a^2-1768=0

a = 5; b = 0; c = -1768;
Δ = b2-4ac
Δ = 02-4·5·(-1768)
Δ = 35360
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:

$\sqrt{\Delta}=\sqrt{35360}=\sqrt{16*2210}=\sqrt{16}*\sqrt{2210}=4\sqrt{2210}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2210}}{2*5}=\frac{0-4\sqrt{2210}}{10}
=-\frac{4\sqrt{2210}}{10}
=-\frac{2\sqrt{2210}}{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2210}}{2*5}=\frac{0+4\sqrt{2210}}{10}
=\frac{4\sqrt{2210}}{10}
=\frac{2\sqrt{2210}}{5}
$