54=(4x+6)(2x)

Solution for 54=(4x+6)(2x) equation:

54=(4x+6)(2x)

We move all terms to the left:

54-((4x+6)(2x))=0


We calculate terms in parentheses: -((4x+6)2x), so:

(4x+6)2x

We multiply parentheses

8x^2+12x

Back to the equation:

-(8x^2+12x)


We get rid of parentheses

-8x^2-12x+54=0

a = -8; b = -12; c = +54;
Δ = b2-4ac
Δ = -122-4·(-8)·54
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{13}}{2*-8}=\frac{12-12\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{13}}{2*-8}=\frac{12+12\sqrt{13}}{-16}
$