3(x^2-22x+114)=0

Solution for 3(x^2-22x+114)=0 equation:

3(x^2-22x+114)=0

We multiply parentheses

3x^2-66x+342=0

a = 3; b = -66; c = +342;
Δ = b2-4ac
Δ = -662-4·3·342
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{7}}{2*3}=\frac{66-6\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{7}}{2*3}=\frac{66+6\sqrt{7}}{6}
$