3x(x+4)=66

Solution for 3x(x+4)=66 equation:

3x(x+4)=66

We move all terms to the left:

3x(x+4)-(66)=0

We multiply parentheses

3x^2+12x-66=0

a = 3; b = 12; c = -66;
Δ = b2-4ac
Δ = 122-4·3·(-66)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{26}}{2*3}=\frac{-12-6\sqrt{26}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{26}}{2*3}=\frac{-12+6\sqrt{26}}{6}
$