185=(x+8)(x+8)-(x-3)(x+3)

Solution for 185=(x+8)(x+8)-(x-3)(x+3) equation:

185=(x+8)(x+8)-(x-3)(x+3)

We move all terms to the left:

185-((x+8)(x+8)-(x-3)(x+3))=0

We multiply parentheses ..

-((+x^2+8x+8x+64)-(x-3)(x+3))+185=0


We calculate terms in parentheses: -((+x^2+8x+8x+64)-(x-3)(x+3)), so:

(+x^2+8x+8x+64)-(x-3)(x+3)

We use the square of the difference formula

(+x^2+8x+8x+64)+x^2+9

We get rid of parentheses

x^2+x^2+8x+8x+64+9

We add all the numbers together, and all the variables

2x^2+16x+73

Back to the equation:

-(2x^2+16x+73)


We get rid of parentheses

-2x^2-16x-73+185=0

We add all the numbers together, and all the variables

-2x^2-16x+112=0

a = -2; b = -16; c = +112;
Δ = b2-4ac
Δ = -162-4·(-2)·112
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-24\sqrt{2}}{2*-2}=\frac{16-24\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+24\sqrt{2}}{2*-2}=\frac{16+24\sqrt{2}}{-4}
$