(16-2x)(26-2x)=200

Solution for (16-2x)(26-2x)=200 equation:

(16-2x)(26-2x)=200

We move all terms to the left:

(16-2x)(26-2x)-(200)=0

We add all the numbers together, and all the variables

(-2x+16)(-2x+26)-200=0

We multiply parentheses ..

(+4x^2-52x-32x+416)-200=0

We get rid of parentheses

4x^2-52x-32x+416-200=0

We add all the numbers together, and all the variables

4x^2-84x+216=0

a = 4; b = -84; c = +216;
Δ = b2-4ac
Δ = -842-4·4·216
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-60}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+60}{2*4}=\frac{144}{8}
=18
$