173=x+x2+x+17

Solution for 173=x+x2+x+17 equation:

173=x+x2+x+17

We move all terms to the left:

173-(x+x2+x+17)=0

We add all the numbers together, and all the variables

-(+2x+x^2+17)+173=0

We get rid of parentheses

-x^2-2x-17+173=0

We add all the numbers together, and all the variables

-1x^2-2x+156=0

a = -1; b = -2; c = +156;
Δ = b2-4ac
Δ = -22-4·(-1)·156
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{157}}{2*-1}=\frac{2-2\sqrt{157}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{157}}{2*-1}=\frac{2+2\sqrt{157}}{-2}
$