x^2-42x-63=0

Solution for x^2-42x-63=0 equation:

x^2-42x-63=0

a = 1; b = -42; c = -63;
Δ = b2-4ac
Δ = -422-4·1·(-63)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-12\sqrt{14}}{2*1}=\frac{42-12\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+12\sqrt{14}}{2*1}=\frac{42+12\sqrt{14}}{2}
$