39=x(10+x)

Solution for 39=x(10+x) equation:

39=x(10+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(x+10))+39=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+39=0

We add all the numbers together, and all the variables

-1x^2-10x+39=0

a = -1; b = -10; c = +39;
Δ = b2-4ac
Δ = -102-4·(-1)·39
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-16}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+16}{2*-1}=\frac{26}{-2}
=-13
$