(30-2x)(12-2x)=208

Solution for (30-2x)(12-2x)=208 equation:

(30-2x)(12-2x)=208

We move all terms to the left:

(30-2x)(12-2x)-(208)=0

We add all the numbers together, and all the variables

(-2x+30)(-2x+12)-208=0

We multiply parentheses ..

(+4x^2-24x-60x+360)-208=0

We get rid of parentheses

4x^2-24x-60x+360-208=0

We add all the numbers together, and all the variables

4x^2-84x+152=0

a = 4; b = -84; c = +152;
Δ = b2-4ac
Δ = -842-4·4·152
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-68}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+68}{2*4}=\frac{152}{8}
=19
$