39*x^2+12*x-4=0

Solution for 39*x^2+12*x-4=0 equation:

39x^2+12x-4=0

a = 39; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·39·(-4)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16\sqrt{3}}{2*39}=\frac{-12-16\sqrt{3}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16\sqrt{3}}{2*39}=\frac{-12+16\sqrt{3}}{78}
$