a^2=176

Solution for a^2=176 equation:

a^2=176

We move all terms to the left:

a^2-(176)=0

a = 1; b = 0; c = -176;
Δ = b2-4ac
Δ = 02-4·1·(-176)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*1}=\frac{0-8\sqrt{11}}{2}
=-\frac{8\sqrt{11}}{2}
=-4\sqrt{11}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*1}=\frac{0+8\sqrt{11}}{2}
=\frac{8\sqrt{11}}{2}
=4\sqrt{11}
$