-4x(x+12)=-22

Solution for -4x(x+12)=-22 equation:

-4x(x+12)=-22

We move all terms to the left:

-4x(x+12)-(-22)=0

We add all the numbers together, and all the variables

-4x(x+12)+22=0

We multiply parentheses

-4x^2-48x+22=0

a = -4; b = -48; c = +22;
Δ = b2-4ac
Δ = -482-4·(-4)·22
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{166}}{2*-4}=\frac{48-4\sqrt{166}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{166}}{2*-4}=\frac{48+4\sqrt{166}}{-8}
$