0=4x^2-23x-6

Solution for 0=4x^2-23x-6 equation:

0=4x^2-23x-6

We move all terms to the left:

0-(4x^2-23x-6)=0

We add all the numbers together, and all the variables

-(4x^2-23x-6)=0

We get rid of parentheses

-4x^2+23x+6=0

a = -4; b = 23; c = +6;
Δ = b2-4ac
Δ = 232-4·(-4)·6
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-25}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+25}{2*-4}=\frac{2}{-8}
=-1/4
$