48+8x-x*x=0

Solution for 48+8x-x*x=0 equation:

48+8x-x*x=0

Wy multiply elements

-1x^2+8x+48=0

a = -1; b = 8; c = +48;
Δ = b2-4ac
Δ = 82-4·(-1)·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*-1}=\frac{8}{-2}
=-4
$