100x-x^2=2475

Solution for 100x-x^2=2475 equation:

100x-x^2=2475

We move all terms to the left:

100x-x^2-(2475)=0

We add all the numbers together, and all the variables

-1x^2+100x-2475=0

a = -1; b = 100; c = -2475;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2475)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10}{2*-1}=\frac{-110}{-2}
=+55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10}{2*-1}=\frac{-90}{-2}
=+45
$