21x-x^2+120=0

Solution for 21x-x^2+120=0 equation:

21x-x^2+120=0

We add all the numbers together, and all the variables

-1x^2+21x+120=0

a = -1; b = 21; c = +120;
Δ = b2-4ac
Δ = 212-4·(-1)·120
Δ = 921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{921}}{2*-1}=\frac{-21-\sqrt{921}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{921}}{2*-1}=\frac{-21+\sqrt{921}}{-2}
$