3(x^2+11x-47)=0

Solution for 3(x^2+11x-47)=0 equation:

3(x^2+11x-47)=0

We multiply parentheses

3x^2+33x-141=0

a = 3; b = 33; c = -141;
Δ = b2-4ac
Δ = 332-4·3·(-141)
Δ = 2781
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:

$\sqrt{\Delta}=\sqrt{2781}=\sqrt{9*309}=\sqrt{9}*\sqrt{309}=3\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{309}}{2*3}=\frac{-33-3\sqrt{309}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{309}}{2*3}=\frac{-33+3\sqrt{309}}{6}
$