10-x(3+x)=x

Solution for 10-x(3+x)=x equation:

10-x(3+x)=x

We move all terms to the left:

10-x(3+x)-(x)=0

We add all the numbers together, and all the variables

-x(x+3)-x+10=0

We add all the numbers together, and all the variables

-1x-x(x+3)+10=0

We multiply parentheses

-x^2-1x-3x+10=0

We add all the numbers together, and all the variables

-1x^2-4x+10=0

a = -1; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-1)·10
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*-1}=\frac{4-2\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*-1}=\frac{4+2\sqrt{14}}{-2}
$