(26+2x)(16-2x)-16*26=18426(16+2x)+2x(16+2x)=184

Solution for (26+2x)(16-2x)-16*26=18426(16+2x)+2x(16+2x)=184 equation:

(26+2x)(16-2x)-16*26=18426(16+2x)+2x(16+2x)=184

We move all terms to the left:

(26+2x)(16-2x)-16*26-(18426(16+2x)+2x(16+2x))=0

We add all the numbers together, and all the variables

(2x+26)(-2x+16)-(18426(2x+16)+2x(2x+16))-16*26=0

We add all the numbers together, and all the variables

(2x+26)(-2x+16)-(18426(2x+16)+2x(2x+16))-416=0

We multiply parentheses ..

(-4x^2+32x-52x+416)-(18426(2x+16)+2x(2x+16))-416=0


We calculate terms in parentheses: -(18426(2x+16)+2x(2x+16)), so:

18426(2x+16)+2x(2x+16)

We multiply parentheses

4x^2+36852x+32x+294816

We add all the numbers together, and all the variables

4x^2+36884x+294816

Back to the equation:

-(4x^2+36884x+294816)


We get rid of parentheses

-4x^2-4x^2+32x-52x-36884x+416-294816-416=0

We add all the numbers together, and all the variables

-8x^2-36904x-294816=0

a = -8; b = -36904; c = -294816;
Δ = b2-4ac
Δ = -369042-4·(-8)·(-294816)
Δ = 1352471104
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:

$\sqrt{\Delta}=\sqrt{1352471104}=\sqrt{64*21132361}=\sqrt{64}*\sqrt{21132361}=8\sqrt{21132361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36904)-8\sqrt{21132361}}{2*-8}=\frac{36904-8\sqrt{21132361}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36904)+8\sqrt{21132361}}{2*-8}=\frac{36904+8\sqrt{21132361}}{-16}
$