(4x+84)(2x-8)=0

Solution for (4x+84)(2x-8)=0 equation:

(4x+84)(2x-8)=0

We multiply parentheses ..

(+8x^2-32x+168x-672)=0

We get rid of parentheses

8x^2-32x+168x-672=0

We add all the numbers together, and all the variables

8x^2+136x-672=0

a = 8; b = 136; c = -672;
Δ = b2-4ac
Δ = 1362-4·8·(-672)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-200}{2*8}=\frac{-336}{16}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+200}{2*8}=\frac{64}{16}
=4
$