(x-11)(x+51)=0

Solution for (x-11)(x+51)=0 equation:

(x-11)(x+51)=0

We multiply parentheses ..

(+x^2+51x-11x-561)=0

We get rid of parentheses

x^2+51x-11x-561=0

We add all the numbers together, and all the variables

x^2+40x-561=0

a = 1; b = 40; c = -561;
Δ = b2-4ac
Δ = 402-4·1·(-561)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-62}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+62}{2*1}=\frac{22}{2}
=11
$