x*(-12+2*x)=3024

Solution for x*(-12+2*x)=3024 equation:

x(-12+2x)=3024

We move all terms to the left:

x(-12+2x)-(3024)=0

We add all the numbers together, and all the variables

x(2x-12)-3024=0

We multiply parentheses

2x^2-12x-3024=0

a = 2; b = -12; c = -3024;
Δ = b2-4ac
Δ = -122-4·2·(-3024)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-156}{2*2}=\frac{-144}{4}
=-36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+156}{2*2}=\frac{168}{4}
=42
$