4a2-3=497

Solution for 4a2-3=497 equation:

4a^2-3=497

We move all terms to the left:

4a^2-3-(497)=0

We add all the numbers together, and all the variables

4a^2-500=0

a = 4; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·4·(-500)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*4}=\frac{0-40\sqrt{5}}{8}
=-\frac{40\sqrt{5}}{8}
=-5\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*4}=\frac{0+40\sqrt{5}}{8}
=\frac{40\sqrt{5}}{8}
=5\sqrt{5}
$