3x^2-18x-5=42

Solution for 3x^2-18x-5=42 equation:

3x^2-18x-5=42

We move all terms to the left:

3x^2-18x-5-(42)=0

We add all the numbers together, and all the variables

3x^2-18x-47=0

a = 3; b = -18; c = -47;
Δ = b2-4ac
Δ = -182-4·3·(-47)
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{222}}{2*3}=\frac{18-2\sqrt{222}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{222}}{2*3}=\frac{18+2\sqrt{222}}{6}
$