-x^2+74x-1200=0

Solution for -x^2+74x-1200=0 equation:

-x^2+74x-1200=0

We add all the numbers together, and all the variables

-1x^2+74x-1200=0

a = -1; b = 74; c = -1200;
Δ = b2-4ac
Δ = 742-4·(-1)·(-1200)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-26}{2*-1}=\frac{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+26}{2*-1}=\frac{-48}{-2}
=+24
$