(x+8)2=x(x+20)+42

Solution for (x+8)2=x(x+20)+42 equation:

(x+8)2=x(x+20)+42

We move all terms to the left:

(x+8)2-(x(x+20)+42)=0

We multiply parentheses

2x-(x(x+20)+42)+16=0


We calculate terms in parentheses: -(x(x+20)+42), so:

x(x+20)+42

We multiply parentheses

x^2+20x+42

Back to the equation:

-(x^2+20x+42)


We get rid of parentheses

-x^2+2x-20x-42+16=0

We add all the numbers together, and all the variables

-1x^2-18x-26=0

a = -1; b = -18; c = -26;
Δ = b2-4ac
Δ = -182-4·(-1)·(-26)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{55}}{2*-1}=\frac{18-2\sqrt{55}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{55}}{2*-1}=\frac{18+2\sqrt{55}}{-2}
$