x(x-7)=20

Solution for x(x-7)=20 equation:

x(x-7)=20

We move all terms to the left:

x(x-7)-(20)=0

We multiply parentheses

x^2-7x-20=0

a = 1; b = -7; c = -20;
Δ = b2-4ac
Δ = -72-4·1·(-20)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{129}}{2*1}=\frac{7-\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*1}=\frac{7+\sqrt{129}}{2}
$