6x+4x(12-x)=57

Solution for 6x+4x(12-x)=57 equation:

6x+4x(12-x)=57

We move all terms to the left:

6x+4x(12-x)-(57)=0

We add all the numbers together, and all the variables

6x+4x(-1x+12)-57=0

We multiply parentheses

-4x^2+6x+48x-57=0

We add all the numbers together, and all the variables

-4x^2+54x-57=0

a = -4; b = 54; c = -57;
Δ = b2-4ac
Δ = 542-4·(-4)·(-57)
Δ = 2004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{501}}{2*-4}=\frac{-54-2\sqrt{501}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{501}}{2*-4}=\frac{-54+2\sqrt{501}}{-8}
$