3x(x+8)=32

Solution for 3x(x+8)=32 equation:

3x(x+8)=32

We move all terms to the left:

3x(x+8)-(32)=0

We multiply parentheses

3x^2+24x-32=0

a = 3; b = 24; c = -32;
Δ = b2-4ac
Δ = 242-4·3·(-32)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{15}}{2*3}=\frac{-24-8\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{15}}{2*3}=\frac{-24+8\sqrt{15}}{6}
$