2x(x+17)=0

Solution for 2x(x+17)=0 equation:

2x(x+17)=0

We multiply parentheses

2x^2+34x=0

a = 2; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·2·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*2}=\frac{-68}{4}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*2}=\frac{0}{4}
=0
$