8a^2=42

Solution for 8a^2=42 equation:

8a^2=42

We move all terms to the left:

8a^2-(42)=0

a = 8; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·8·(-42)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{21}}{2*8}=\frac{0-8\sqrt{21}}{16}
=-\frac{8\sqrt{21}}{16}
=-\frac{\sqrt{21}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*8}=\frac{0+8\sqrt{21}}{16}
=\frac{8\sqrt{21}}{16}
=\frac{\sqrt{21}}{2}
$