(x+11)(x+23)=589

Solution for (x+11)(x+23)=589 equation:

(x+11)(x+23)=589

We move all terms to the left:

(x+11)(x+23)-(589)=0

We multiply parentheses ..

(+x^2+23x+11x+253)-589=0

We get rid of parentheses

x^2+23x+11x+253-589=0

We add all the numbers together, and all the variables

x^2+34x-336=0

a = 1; b = 34; c = -336;
Δ = b2-4ac
Δ = 342-4·1·(-336)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-50}{2*1}=\frac{-84}{2}
=-42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+50}{2*1}=\frac{16}{2}
=8
$