(16+2x)(30+2x)=1040

Solution for (16+2x)(30+2x)=1040 equation:

(16+2x)(30+2x)=1040

We move all terms to the left:

(16+2x)(30+2x)-(1040)=0

We add all the numbers together, and all the variables

(2x+16)(2x+30)-1040=0

We multiply parentheses ..

(+4x^2+60x+32x+480)-1040=0

We get rid of parentheses

4x^2+60x+32x+480-1040=0

We add all the numbers together, and all the variables

4x^2+92x-560=0

a = 4; b = 92; c = -560;
Δ = b2-4ac
Δ = 922-4·4·(-560)
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{-(92)-132}{2*4}=\frac{-224}{8}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+132}{2*4}=\frac{40}{8}
=5
$