12x^2+243x-189=0

Solution for 12x^2+243x-189=0 equation:

12x^2+243x-189=0

a = 12; b = 243; c = -189;
Δ = b2-4ac
Δ = 2432-4·12·(-189)
Δ = 68121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{68121}=261$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-261}{2*12}=\frac{-504}{24}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+261}{2*12}=\frac{18}{24}
=3/4
$