120x-x^2=2700

Solution for 120x-x^2=2700 equation:

120x-x^2=2700

We move all terms to the left:

120x-x^2-(2700)=0

We add all the numbers together, and all the variables

-1x^2+120x-2700=0

a = -1; b = 120; c = -2700;
Δ = b2-4ac
Δ = 1202-4·(-1)·(-2700)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-60}{2*-1}=\frac{-180}{-2}
=+90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+60}{2*-1}=\frac{-60}{-2}
=+30
$