(10+8)8=(9+x)x

Solution for (10+8)8=(9+x)x equation:

(10+8)8=(9+x)x

We move all terms to the left:

(10+8)8-((9+x)x)=0

We add all the numbers together, and all the variables

-((x+9)x)+188=0


We calculate terms in parentheses: -((x+9)x), so:

(x+9)x

We multiply parentheses

x^2+9x

Back to the equation:

-(x^2+9x)


We get rid of parentheses

-x^2-9x+188=0

We add all the numbers together, and all the variables

-1x^2-9x+188=0

a = -1; b = -9; c = +188;
Δ = b2-4ac
Δ = -92-4·(-1)·188
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7\sqrt{17}}{2*-1}=\frac{9-7\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7\sqrt{17}}{2*-1}=\frac{9+7\sqrt{17}}{-2}
$