12x^2-38x-14=0

Solution for 12x^2-38x-14=0 equation:

12x^2-38x-14=0

a = 12; b = -38; c = -14;
Δ = b2-4ac
Δ = -382-4·12·(-14)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-46}{2*12}=\frac{-8}{24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+46}{2*12}=\frac{84}{24}
=3+1/2
$