2x^2+12x-684=0

Solution for 2x^2+12x-684=0 equation:

2x^2+12x-684=0

a = 2; b = 12; c = -684;
Δ = b2-4ac
Δ = 122-4·2·(-684)
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{39}}{2*2}=\frac{-12-12\sqrt{39}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{39}}{2*2}=\frac{-12+12\sqrt{39}}{4}
$