12x^2+27x-60=0

Solution for 12x^2+27x-60=0 equation:

12x^2+27x-60=0

a = 12; b = 27; c = -60;
Δ = b2-4ac
Δ = 272-4·12·(-60)
Δ = 3609
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:

$\sqrt{\Delta}=\sqrt{3609}=\sqrt{9*401}=\sqrt{9}*\sqrt{401}=3\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{401}}{2*12}=\frac{-27-3\sqrt{401}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{401}}{2*12}=\frac{-27+3\sqrt{401}}{24}
$