0=6x^2+23x-4

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

0=6x^2+23x-4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -6; b = -23; c = +4;
Δ = b2-4ac
Δ = -232-4·(-6)·4
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*-6}=\frac{-2}{-12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*-6}=\frac{48}{-12}
=-4
$