2x+x^2=174

Solution for 2x+x^2=174 equation:

2x+x^2=174

We move all terms to the left:

2x+x^2-(174)=0

a = 1; b = 2; c = -174;
Δ = b2-4ac
Δ = 22-4·1·(-174)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10\sqrt{7}}{2*1}=\frac{-2-10\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10\sqrt{7}}{2*1}=\frac{-2+10\sqrt{7}}{2}
$