(x-10)x=171

Solution for (x-10)x=171 equation:

(x-10)x=171

We move all terms to the left:

(x-10)x-(171)=0

We multiply parentheses

x^2-10x-171=0

a = 1; b = -10; c = -171;
Δ = b2-4ac
Δ = -102-4·1·(-171)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-28}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+28}{2*1}=\frac{38}{2}
=19
$