x(x-7)=x-7+x+2+x+9

Solution for x(x-7)=x-7+x+2+x+9 equation:

x(x-7)=x-7+x+2+x+9

We move all terms to the left:

x(x-7)-(x-7+x+2+x+9)=0

We add all the numbers together, and all the variables

x(x-7)-(3x+4)=0

We multiply parentheses

x^2-7x-(3x+4)=0

We get rid of parentheses

x^2-7x-3x-4=0

We add all the numbers together, and all the variables

x^2-10x-4=0

a = 1; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·1·(-4)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*1}=\frac{10-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*1}=\frac{10+2\sqrt{29}}{2}
$