7x(-x-12)=32-4x

Solution for 7x(-x-12)=32-4x equation:

7x(-x-12)=32-4x

We move all terms to the left:

7x(-x-12)-(32-4x)=0

We add all the numbers together, and all the variables

7x(-1x-12)-(-4x+32)=0

We multiply parentheses

-7x^2-84x-(-4x+32)=0

We get rid of parentheses

-7x^2-84x+4x-32=0

We add all the numbers together, and all the variables

-7x^2-80x-32=0

a = -7; b = -80; c = -32;
Δ = b2-4ac
Δ = -802-4·(-7)·(-32)
Δ = 5504
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:

$\sqrt{\Delta}=\sqrt{5504}=\sqrt{64*86}=\sqrt{64}*\sqrt{86}=8\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{86}}{2*-7}=\frac{80-8\sqrt{86}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{86}}{2*-7}=\frac{80+8\sqrt{86}}{-14}
$