4a^2+5=385

Solution for 4a^2+5=385 equation:

4a^2+5=385

We move all terms to the left:

4a^2+5-(385)=0

We add all the numbers together, and all the variables

4a^2-380=0

a = 4; b = 0; c = -380;
Δ = b2-4ac
Δ = 02-4·4·(-380)
Δ = 6080
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:

$\sqrt{\Delta}=\sqrt{6080}=\sqrt{64*95}=\sqrt{64}*\sqrt{95}=8\sqrt{95}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{95}}{2*4}=\frac{0-8\sqrt{95}}{8}
=-\frac{8\sqrt{95}}{8}
=-\sqrt{95}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{95}}{2*4}=\frac{0+8\sqrt{95}}{8}
=\frac{8\sqrt{95}}{8}
=\sqrt{95}
$