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

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

4x*x-5x-12=0

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-5x-12=0

a = 4; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·4·(-12)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*4}=\frac{5-\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*4}=\frac{5+\sqrt{217}}{8}
$