1200=10x+x*x

Solution for 1200=10x+x*x equation:

1200=10x+x*x

We move all terms to the left:

1200-(10x+x*x)=0

We add all the numbers together, and all the variables

-(+10x+x*x)+1200=0

We get rid of parentheses

-10x-x*x+1200=0

Wy multiply elements

-1x^2-10x+1200=0

a = -1; b = -10; c = +1200;
Δ = b2-4ac
Δ = -102-4·(-1)·1200
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-70}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+70}{2*-1}=\frac{80}{-2}
=-40
$