-x^2+50x-225=300

Solution for -x^2+50x-225=300 equation:

-x^2+50x-225=300

We move all terms to the left:

-x^2+50x-225-(300)=0

We add all the numbers together, and all the variables

-1x^2+50x-525=0

a = -1; b = 50; c = -525;
Δ = b2-4ac
Δ = 502-4·(-1)·(-525)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-20}{2*-1}=\frac{-70}{-2}
=+35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+20}{2*-1}=\frac{-30}{-2}
=+15
$