(16+2x)(9+2x)-144=200

Solution for (16+2x)(9+2x)-144=200 equation:

(16+2x)(9+2x)-144=200

We move all terms to the left:

(16+2x)(9+2x)-144-(200)=0

We add all the numbers together, and all the variables

(2x+16)(2x+9)-144-200=0

We add all the numbers together, and all the variables

(2x+16)(2x+9)-344=0

We multiply parentheses ..

(+4x^2+18x+32x+144)-344=0

We get rid of parentheses

4x^2+18x+32x+144-344=0

We add all the numbers together, and all the variables

4x^2+50x-200=0

a = 4; b = 50; c = -200;
Δ = b2-4ac
Δ = 502-4·4·(-200)
Δ = 5700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{57}}{2*4}=\frac{-50-10\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{57}}{2*4}=\frac{-50+10\sqrt{57}}{8}
$