x^2-10x=71

Solution for x^2-10x=71 equation:

x^2-10x=71

We move all terms to the left:

x^2-10x-(71)=0

a = 1; b = -10; c = -71;
Δ = b2-4ac
Δ = -102-4·1·(-71)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{6}}{2*1}=\frac{10-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{6}}{2*1}=\frac{10+8\sqrt{6}}{2}
$