x(6x+23)=4

Solution for x(6x+23)=4 equation:

x(6x+23)=4

We move all terms to the left:

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

We multiply 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{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+25}{2*6}=\frac{2}{12}
=1/6
$