x(2x+17)=174

Solution for x(2x+17)=174 equation:

x(2x+17)=174

We move all terms to the left:

x(2x+17)-(174)=0

We multiply parentheses

2x^2+17x-174=0

a = 2; b = 17; c = -174;
Δ = b2-4ac
Δ = 172-4·2·(-174)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-41}{2*2}=\frac{-58}{4}
=-14+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+41}{2*2}=\frac{24}{4}
=6
$