120x-x^2-575=0

Solution for 120x-x^2-575=0 equation:

120x-x^2-575=0

We add all the numbers together, and all the variables

-1x^2+120x-575=0

a = -1; b = 120; c = -575;
Δ = b2-4ac
Δ = 1202-4·(-1)·(-575)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-110}{2*-1}=\frac{-230}{-2}
=+115
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+110}{2*-1}=\frac{-10}{-2}
=+5
$