27x+108+27x-108=5(x^2-16)

Solution for 27x+108+27x-108=5(x^2-16) equation:

27x+108+27x-108=5(x^2-16)

We move all terms to the left:

27x+108+27x-108-(5(x^2-16))=0

We add all the numbers together, and all the variables

54x-(5(x^2-16))=0


We calculate terms in parentheses: -(5(x^2-16)), so:

5(x^2-16)

We multiply parentheses

5x^2-80

Back to the equation:

-(5x^2-80)


We get rid of parentheses

-5x^2+54x+80=0

a = -5; b = 54; c = +80;
Δ = b2-4ac
Δ = 542-4·(-5)·80
Δ = 4516
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:

$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{1129}}{2*-5}=\frac{-54-2\sqrt{1129}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{1129}}{2*-5}=\frac{-54+2\sqrt{1129}}{-10}
$