(-4)(x+4)(x-7)=33

Solution for (-4)(x+4)(x-7)=33 equation:

(-4)(x+4)(x-7)=33

We move all terms to the left:

(-4)(x+4)(x-7)-(33)=0

We multiply parentheses ..

(-4x-16)(x-7)-33=0

We multiply parentheses ..

(-4x^2+28x-16x+112)-33=0

We get rid of parentheses

-4x^2+28x-16x+112-33=0

We add all the numbers together, and all the variables

-4x^2+12x+79=0

a = -4; b = 12; c = +79;
Δ = b2-4ac
Δ = 122-4·(-4)·79
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{22}}{2*-4}=\frac{-12-8\sqrt{22}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{22}}{2*-4}=\frac{-12+8\sqrt{22}}{-8}
$