x^2-42x-162=0

Solution for x^2-42x-162=0 equation:

x^2-42x-162=0

a = 1; b = -42; c = -162;
Δ = b2-4ac
Δ = -422-4·1·(-162)
Δ = 2412
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:

$\sqrt{\Delta}=\sqrt{2412}=\sqrt{36*67}=\sqrt{36}*\sqrt{67}=6\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{67}}{2*1}=\frac{42-6\sqrt{67}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{67}}{2*1}=\frac{42+6\sqrt{67}}{2}
$