x*x-14=176

Solution for x*x-14=176 equation:

x*x-14=176

We move all terms to the left:

x*x-14-(176)=0

We add all the numbers together, and all the variables

x*x-190=0

Wy multiply elements

x^2-190=0

a = 1; b = 0; c = -190;
Δ = b2-4ac
Δ = 02-4·1·(-190)
Δ = 760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*1}=\frac{0-2\sqrt{190}}{2}
=-\frac{2\sqrt{190}}{2}
=-\sqrt{190}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*1}=\frac{0+2\sqrt{190}}{2}
=\frac{2\sqrt{190}}{2}
=\sqrt{190}
$