12x^2-8x-48=0

Solution for 12x^2-8x-48=0 equation:

12x^2-8x-48=0

a = 12; b = -8; c = -48;
Δ = b2-4ac
Δ = -82-4·12·(-48)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{37}}{2*12}=\frac{8-8\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{37}}{2*12}=\frac{8+8\sqrt{37}}{24}
$