(30+2x)(12+2x)=1288

Solution for (30+2x)(12+2x)=1288 equation:

(30+2x)(12+2x)=1288

We move all terms to the left:

(30+2x)(12+2x)-(1288)=0

We add all the numbers together, and all the variables

(2x+30)(2x+12)-1288=0

We multiply parentheses ..

(+4x^2+24x+60x+360)-1288=0

We get rid of parentheses

4x^2+24x+60x+360-1288=0

We add all the numbers together, and all the variables

4x^2+84x-928=0

a = 4; b = 84; c = -928;
Δ = b2-4ac
Δ = 842-4·4·(-928)
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-148}{2*4}=\frac{-232}{8}
=-29
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+148}{2*4}=\frac{64}{8}
=8
$