x(x+26)=456

Solution for x(x+26)=456 equation:

x(x+26)=456

We move all terms to the left:

x(x+26)-(456)=0

We multiply parentheses

x^2+26x-456=0

a = 1; b = 26; c = -456;
Δ = b2-4ac
Δ = 262-4·1·(-456)
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{-(26)-50}{2*1}=\frac{-76}{2}
=-38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+50}{2*1}=\frac{24}{2}
=12
$