12x^2-105x-27=0

Solution for 12x^2-105x-27=0 equation:

12x^2-105x-27=0

a = 12; b = -105; c = -27;
Δ = b2-4ac
Δ = -1052-4·12·(-27)
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-111}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+111}{2*12}=\frac{216}{24}
=9
$