12x^2-60x-48=0

Solution for 12x^2-60x-48=0 equation:

12x^2-60x-48=0

a = 12; b = -60; c = -48;
Δ = b2-4ac
Δ = -602-4·12·(-48)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{41}}{2*12}=\frac{60-12\sqrt{41}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{41}}{2*12}=\frac{60+12\sqrt{41}}{24}
$