6200=x^2-10+4200

Solution for 6200=x^2-10+4200 equation:

6200=x^2-10+4200

We move all terms to the left:

6200-(x^2-10+4200)=0

We get rid of parentheses

-x^2+10-4200+6200=0

We add all the numbers together, and all the variables

-1x^2+2010=0

a = -1; b = 0; c = +2010;
Δ = b2-4ac
Δ = 02-4·(-1)·2010
Δ = 8040
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:

$\sqrt{\Delta}=\sqrt{8040}=\sqrt{4*2010}=\sqrt{4}*\sqrt{2010}=2\sqrt{2010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2010}}{2*-1}=\frac{0-2\sqrt{2010}}{-2}
=-\frac{2\sqrt{2010}}{-2}
=-\frac{\sqrt{2010}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2010}}{2*-1}=\frac{0+2\sqrt{2010}}{-2}
=\frac{2\sqrt{2010}}{-2}
=\frac{\sqrt{2010}}{-1}
$