5x-x^2=-50

Solution for 5x-x^2=-50 equation:

5x-x^2=-50

We move all terms to the left:

5x-x^2-(-50)=0

We add all the numbers together, and all the variables

-1x^2+5x+50=0

a = -1; b = 5; c = +50;
Δ = b2-4ac
Δ = 52-4·(-1)·50
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*-1}=\frac{10}{-2}
=-5
$