12x^2-23x-77=0

Solution for 12x^2-23x-77=0 equation:

12x^2-23x-77=0

a = 12; b = -23; c = -77;
Δ = b2-4ac
Δ = -232-4·12·(-77)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-65}{2*12}=\frac{-42}{24}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+65}{2*12}=\frac{88}{24}
=3+2/3
$