12*x*x-4*x-5=0

Solution for 12*x*x-4*x-5=0 equation:

12x*x-4x-5=0

We add all the numbers together, and all the variables

-4x+12x*x-5=0

Wy multiply elements

12x^2-4x-5=0

a = 12; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·12·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*12}=\frac{20}{24}
=5/6
$