(30+2x)(24+x)=1080

Solution for (30+2x)(24+x)=1080 equation:

(30+2x)(24+x)=1080

We move all terms to the left:

(30+2x)(24+x)-(1080)=0

We add all the numbers together, and all the variables

(2x+30)(x+24)-1080=0

We multiply parentheses ..

(+2x^2+48x+30x+720)-1080=0

We get rid of parentheses

2x^2+48x+30x+720-1080=0

We add all the numbers together, and all the variables

2x^2+78x-360=0

a = 2; b = 78; c = -360;
Δ = b2-4ac
Δ = 782-4·2·(-360)
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{249}}{2*2}=\frac{-78-6\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{249}}{2*2}=\frac{-78+6\sqrt{249}}{4}
$