(30-2x)(24-2x)=112

Solution for (30-2x)(24-2x)=112 equation:

(30-2x)(24-2x)=112

We move all terms to the left:

(30-2x)(24-2x)-(112)=0

We add all the numbers together, and all the variables

(-2x+30)(-2x+24)-112=0

We multiply parentheses ..

(+4x^2-48x-60x+720)-112=0

We get rid of parentheses

4x^2-48x-60x+720-112=0

We add all the numbers together, and all the variables

4x^2-108x+608=0

a = 4; b = -108; c = +608;
Δ = b2-4ac
Δ = -1082-4·4·608
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-44}{2*4}=\frac{64}{8}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+44}{2*4}=\frac{152}{8}
=19
$