684=2x^2+18x

Solution for 684=2x^2+18x equation:

684=2x^2+18x

We move all terms to the left:

684-(2x^2+18x)=0

We get rid of parentheses

-2x^2-18x+684=0

a = -2; b = -18; c = +684;
Δ = b2-4ac
Δ = -182-4·(-2)·684
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{161}}{2*-2}=\frac{18-6\sqrt{161}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{161}}{2*-2}=\frac{18+6\sqrt{161}}{-4}
$