9x^2-4x-12=0

Solution for 9x^2-4x-12=0 equation:

9x^2-4x-12=0

a = 9; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·9·(-12)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{7}}{2*9}=\frac{4-8\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{7}}{2*9}=\frac{4+8\sqrt{7}}{18}
$