X^2-54x-71=0

Solution for X^2-54x-71=0 equation:

X^2-54X-71=0

a = 1; b = -54; c = -71;
Δ = b2-4ac
Δ = -542-4·1·(-71)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-40\sqrt{2}}{2*1}=\frac{54-40\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+40\sqrt{2}}{2*1}=\frac{54+40\sqrt{2}}{2}
$