X^2-42x-40=0

Solution for X^2-42x-40=0 equation:

X^2-42X-40=0

a = 1; b = -42; c = -40;
Δ = b2-4ac
Δ = -422-4·1·(-40)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{481}}{2*1}=\frac{42-2\sqrt{481}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{481}}{2*1}=\frac{42+2\sqrt{481}}{2}
$