23=x(x+5)

Solution for 23=x(x+5) equation:

23=x(x+5)

We move all terms to the left:

23-(x(x+5))=0


We calculate terms in parentheses: -(x(x+5)), so:

x(x+5)

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+23=0

We add all the numbers together, and all the variables

-1x^2-5x+23=0

a = -1; b = -5; c = +23;
Δ = b2-4ac
Δ = -52-4·(-1)·23
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{13}}{2*-1}=\frac{5-3\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{13}}{2*-1}=\frac{5+3\sqrt{13}}{-2}
$