49x-x^2-450=0

Solution for 49x-x^2-450=0 equation:

49x-x^2-450=0

We add all the numbers together, and all the variables

-1x^2+49x-450=0

a = -1; b = 49; c = -450;
Δ = b2-4ac
Δ = 492-4·(-1)·(-450)
Δ = 601
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{-(49)-\sqrt{601}}{2*-1}=\frac{-49-\sqrt{601}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{601}}{2*-1}=\frac{-49+\sqrt{601}}{-2}
$