x(x+23)=54

Solution for x(x+23)=54 equation:

x(x+23)=54

We move all terms to the left:

x(x+23)-(54)=0

We multiply parentheses

x^2+23x-54=0

a = 1; b = 23; c = -54;
Δ = b2-4ac
Δ = 232-4·1·(-54)
Δ = 745
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{-(23)-\sqrt{745}}{2*1}=\frac{-23-\sqrt{745}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{745}}{2*1}=\frac{-23+\sqrt{745}}{2}
$