12a^2-23a-16=0

Solution for 12a^2-23a-16=0 equation:

12a^2-23a-16=0

a = 12; b = -23; c = -16;
Δ = b2-4ac
Δ = -232-4·12·(-16)
Δ = 1297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{1297}}{2*12}=\frac{23-\sqrt{1297}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1297}}{2*12}=\frac{23+\sqrt{1297}}{24}
$