x(x+1)=17-x

Solution for x(x+1)=17-x equation:

x(x+1)=17-x

We move all terms to the left:

x(x+1)-(17-x)=0

We add all the numbers together, and all the variables

x(x+1)-(-1x+17)=0

We multiply parentheses

x^2+x-(-1x+17)=0

We get rid of parentheses

x^2+x+1x-17=0

We add all the numbers together, and all the variables

x^2+2x-17=0

a = 1; b = 2; c = -17;
Δ = b2-4ac
Δ = 22-4·1·(-17)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{2}}{2*1}=\frac{-2-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{2}}{2*1}=\frac{-2+6\sqrt{2}}{2}
$