4a^2-106=0

Solution for 4a^2-106=0 equation:

4a^2-106=0

a = 4; b = 0; c = -106;
Δ = b2-4ac
Δ = 02-4·4·(-106)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{106}}{2*4}=\frac{0-4\sqrt{106}}{8}
=-\frac{4\sqrt{106}}{8}
=-\frac{\sqrt{106}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{106}}{2*4}=\frac{0+4\sqrt{106}}{8}
=\frac{4\sqrt{106}}{8}
=\frac{\sqrt{106}}{2}
$