x(x-21)=-68

Solution for x(x-21)=-68 equation:

x(x-21)=-68

We move all terms to the left:

x(x-21)-(-68)=0

We add all the numbers together, and all the variables

x(x-21)+68=0

We multiply parentheses

x^2-21x+68=0

a = 1; b = -21; c = +68;
Δ = b2-4ac
Δ = -212-4·1·68
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-13}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+13}{2*1}=\frac{34}{2}
=17
$