-x^2+10x+1200=0

Solution for -x^2+10x+1200=0 equation:

-x^2+10x+1200=0

We add all the numbers together, and all the variables

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