22=x(10+x)

Solution for 22=x(10+x) equation:

22=x(10+x)

We move all terms to the left:

22-(x(10+x))=0

We add all the numbers together, and all the variables

-(x(x+10))+22=0


We calculate terms in parentheses: -(x(x+10)), so:

x(x+10)

We multiply parentheses

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

-x^2-10x+22=0

We add all the numbers together, and all the variables

-1x^2-10x+22=0

a = -1; b = -10; c = +22;
Δ = b2-4ac
Δ = -102-4·(-1)·22
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{47}}{2*-1}=\frac{10-2\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{47}}{2*-1}=\frac{10+2\sqrt{47}}{-2}
$