12x2-17x-5=0

Solution for 12x2-17x-5=0 equation:

12x^2-17x-5=0

a = 12; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·12·(-5)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*12}=\frac{-6}{24}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*12}=\frac{40}{24}
=1+2/3
$