-x^2+105x-300=1700

Solution for -x^2+105x-300=1700 equation:

-x^2+105x-300=1700

We move all terms to the left:

-x^2+105x-300-(1700)=0

We add all the numbers together, and all the variables

-1x^2+105x-2000=0

a = -1; b = 105; c = -2000;
Δ = b2-4ac
Δ = 1052-4·(-1)·(-2000)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-55}{2*-1}=\frac{-160}{-2}
=+80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+55}{2*-1}=\frac{-50}{-2}
=+25
$