54=(x+5)xX

Solution for 54=(x+5)xX equation:

54=(x+5)xx

We move all terms to the left:

54-((x+5)xx)=0


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

(x+5)xx

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+54=0

We add all the numbers together, and all the variables

-1x^2-5x+54=0

a = -1; b = -5; c = +54;
Δ = b2-4ac
Δ = -52-4·(-1)·54
Δ = 241
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{-(-5)-\sqrt{241}}{2*-1}=\frac{5-\sqrt{241}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*-1}=\frac{5+\sqrt{241}}{-2}
$