x(x-32)=2769

Solution for x(x-32)=2769 equation:

x(x-32)=2769

We move all terms to the left:

x(x-32)-(2769)=0

We multiply parentheses

x^2-32x-2769=0

a = 1; b = -32; c = -2769;
Δ = b2-4ac
Δ = -322-4·1·(-2769)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-110}{2*1}=\frac{-78}{2}
=-39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+110}{2*1}=\frac{142}{2}
=71
$