-x^2+105x-1050=1550

Solution for -x^2+105x-1050=1550 equation:

-x^2+105x-1050=1550

We move all terms to the left:

-x^2+105x-1050-(1550)=0

We add all the numbers together, and all the variables

-1x^2+105x-2600=0

a = -1; b = 105; c = -2600;
Δ = b2-4ac
Δ = 1052-4·(-1)·(-2600)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-25}{2*-1}=\frac{-130}{-2}
=+65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+25}{2*-1}=\frac{-80}{-2}
=+40
$