x*(x-20)=84

Solution for x*(x-20)=84 equation:

x(x-20)=84

We move all terms to the left:

x(x-20)-(84)=0

We multiply parentheses

x^2-20x-84=0

a = 1; b = -20; c = -84;
Δ = b2-4ac
Δ = -202-4·1·(-84)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{46}}{2*1}=\frac{20-4\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{46}}{2*1}=\frac{20+4\sqrt{46}}{2}
$