x2-2x(7+x)+7x=0

Solution for x2-2x(7+x)+7x=0 equation:

x2-2x(7+x)+7x=0

We add all the numbers together, and all the variables

x2-2x(x+7)+7x=0

We add all the numbers together, and all the variables

x^2+7x-2x(x+7)=0

We multiply parentheses

x^2-2x^2+7x-14x=0

We add all the numbers together, and all the variables

-1x^2-7x=0

a = -1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-1}=\frac{14}{-2}
=-7
$