12x2-77x-20=0

Solution for 12x2-77x-20=0 equation:

12x^2-77x-20=0

a = 12; b = -77; c = -20;
Δ = b2-4ac
Δ = -772-4·12·(-20)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-83}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+83}{2*12}=\frac{160}{24}
=6+2/3
$