(12+2x)(x)=5184

Solution for (12+2x)(x)=5184 equation:

(12+2x)(x)=5184

We move all terms to the left:

(12+2x)(x)-(5184)=0

We add all the numbers together, and all the variables

(2x+12)x-5184=0

We multiply parentheses

2x^2+12x-5184=0

a = 2; b = 12; c = -5184;
Δ = b2-4ac
Δ = 122-4·2·(-5184)
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-204}{2*2}=\frac{-216}{4}
=-54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+204}{2*2}=\frac{192}{4}
=48
$