23x(x/2-6)=4

Solution for 23x(x/2-6)=4 equation:

23x(x/2-6)=4

We move all terms to the left:

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

We multiply parentheses

23x^2-138x-4=0

a = 23; b = -138; c = -4;
Δ = b2-4ac
Δ = -1382-4·23·(-4)
Δ = 19412
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19412}=\sqrt{4*4853}=\sqrt{4}*\sqrt{4853}=2\sqrt{4853}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4853}}{2*23}=\frac{138-2\sqrt{4853}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4853}}{2*23}=\frac{138+2\sqrt{4853}}{46}
$