19x-x^2=60

Solution for 19x-x^2=60 equation:

19x-x^2=60

We move all terms to the left:

19x-x^2-(60)=0

We add all the numbers together, and all the variables

-1x^2+19x-60=0

a = -1; b = 19; c = -60;
Δ = b2-4ac
Δ = 192-4·(-1)·(-60)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*-1}=\frac{-8}{-2}
=+4
$