187=x*x+6

Solution for 187=x*x+6 equation:

187=x*x+6

We move all terms to the left:

187-(x*x+6)=0

We get rid of parentheses

-x*x-6+187=0

We add all the numbers together, and all the variables

-x*x+181=0

Wy multiply elements

-1x^2+181=0

a = -1; b = 0; c = +181;
Δ = b2-4ac
Δ = 02-4·(-1)·181
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{181}}{2*-1}=\frac{0-2\sqrt{181}}{-2}
=-\frac{2\sqrt{181}}{-2}
=-\frac{\sqrt{181}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{181}}{2*-1}=\frac{0+2\sqrt{181}}{-2}
=\frac{2\sqrt{181}}{-2}
=\frac{\sqrt{181}}{-1}
$