x(12-x)=-160

Solution for x(12-x)=-160 equation:

x(12-x)=-160

We move all terms to the left:

x(12-x)-(-160)=0

We add all the numbers together, and all the variables

x(-1x+12)-(-160)=0

We add all the numbers together, and all the variables

x(-1x+12)+160=0

We multiply parentheses

-1x^2+12x+160=0

a = -1; b = 12; c = +160;
Δ = b2-4ac
Δ = 122-4·(-1)·160
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*-1}=\frac{16}{-2}
=-8
$