(30+2x)(12+2x)=1008

Solution for (30+2x)(12+2x)=1008 equation:

(30+2x)(12+2x)=1008

We move all terms to the left:

(30+2x)(12+2x)-(1008)=0

We add all the numbers together, and all the variables

(2x+30)(2x+12)-1008=0

We multiply parentheses ..

(+4x^2+24x+60x+360)-1008=0

We get rid of parentheses

4x^2+24x+60x+360-1008=0

We add all the numbers together, and all the variables

4x^2+84x-648=0

a = 4; b = 84; c = -648;
Δ = b2-4ac
Δ = 842-4·4·(-648)
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-132}{2*4}=\frac{-216}{8}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+132}{2*4}=\frac{48}{8}
=6
$