3x(x+8)=24x+768

Solution for 3x(x+8)=24x+768 equation:

3x(x+8)=24x+768

We move all terms to the left:

3x(x+8)-(24x+768)=0

We multiply parentheses

3x^2+24x-(24x+768)=0

We get rid of parentheses

3x^2+24x-24x-768=0

We add all the numbers together, and all the variables

3x^2-768=0

a = 3; b = 0; c = -768;
Δ = b2-4ac
Δ = 02-4·3·(-768)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*3}=\frac{-96}{6}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*3}=\frac{96}{6}
=16
$