x(x-5x)=27(-x-4)

Solution for x(x-5x)=27(-x-4) equation:

x(x-5x)=27(-x-4)

We move all terms to the left:

x(x-5x)-(27(-x-4))=0

We add all the numbers together, and all the variables

x(-4x)-(27(-1x-4))=0

We multiply parentheses

-4x^2-(27(-1x-4))=0


We calculate terms in parentheses: -(27(-1x-4)), so:

27(-1x-4)

We multiply parentheses

-27x-108

Back to the equation:

-(-27x-108)


We get rid of parentheses

-4x^2+27x+108=0

a = -4; b = 27; c = +108;
Δ = b2-4ac
Δ = 272-4·(-4)·108
Δ = 2457
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:

$\sqrt{\Delta}=\sqrt{2457}=\sqrt{9*273}=\sqrt{9}*\sqrt{273}=3\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{273}}{2*-4}=\frac{-27-3\sqrt{273}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{273}}{2*-4}=\frac{-27+3\sqrt{273}}{-8}
$