X2-11x-42=2

Solution for X2-11x-42=2 equation:

X2-11X-42=2

We move all terms to the left:

X2-11X-42-(2)=0

We add all the numbers together, and all the variables

X^2-11X-44=0

a = 1; b = -11; c = -44;
Δ = b2-4ac
Δ = -112-4·1·(-44)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{33}}{2*1}=\frac{11-3\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{33}}{2*1}=\frac{11+3\sqrt{33}}{2}
$