-3(x^2-14x+47)+2=0

Solution for -3(x^2-14x+47)+2=0 equation:

-3(x^2-14x+47)+2=0

We multiply parentheses

-3x^2+42x-141+2=0

We add all the numbers together, and all the variables

-3x^2+42x-139=0

a = -3; b = 42; c = -139;
Δ = b2-4ac
Δ = 422-4·(-3)·(-139)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{6}}{2*-3}=\frac{-42-4\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{6}}{2*-3}=\frac{-42+4\sqrt{6}}{-6}
$