x2-23x=-71

Solution for x2-23x=-71 equation:

x2-23x=-71

We move all terms to the left:

x2-23x-(-71)=0

We add all the numbers together, and all the variables

x^2-23x+71=0

a = 1; b = -23; c = +71;
Δ = b2-4ac
Δ = -232-4·1·71
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7\sqrt{5}}{2*1}=\frac{23-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7\sqrt{5}}{2*1}=\frac{23+7\sqrt{5}}{2}
$