x(5x-12)=(x+54)

Solution for x(5x-12)=(x+54) equation:

x(5x-12)=(x+54)

We move all terms to the left:

x(5x-12)-((x+54))=0

We multiply parentheses

5x^2-12x-((x+54))=0


We calculate terms in parentheses: -((x+54)), so:

(x+54)

We get rid of parentheses

x+54

Back to the equation:

-(x+54)


We get rid of parentheses

5x^2-12x-x-54=0

We add all the numbers together, and all the variables

5x^2-13x-54=0

a = 5; b = -13; c = -54;
Δ = b2-4ac
Δ = -132-4·5·(-54)
Δ = 1249
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{-(-13)-\sqrt{1249}}{2*5}=\frac{13-\sqrt{1249}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1249}}{2*5}=\frac{13+\sqrt{1249}}{10}
$