3x^2+66x+384=600

Solution for 3x^2+66x+384=600 equation:

3x^2+66x+384=600

We move all terms to the left:

3x^2+66x+384-(600)=0

We add all the numbers together, and all the variables

3x^2+66x-216=0

a = 3; b = 66; c = -216;
Δ = b2-4ac
Δ = 662-4·3·(-216)
Δ = 6948
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:

$\sqrt{\Delta}=\sqrt{6948}=\sqrt{36*193}=\sqrt{36}*\sqrt{193}=6\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{193}}{2*3}=\frac{-66-6\sqrt{193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{193}}{2*3}=\frac{-66+6\sqrt{193}}{6}
$