4=(3x-24)2x

Solution for 4=(3x-24)2x equation:

4=(3x-24)2x

We move all terms to the left:

4-((3x-24)2x)=0


We calculate terms in parentheses: -((3x-24)2x), so:

(3x-24)2x

We multiply parentheses

6x^2-48x

Back to the equation:

-(6x^2-48x)


We get rid of parentheses

-6x^2+48x+4=0

a = -6; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·(-6)·4
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-20\sqrt{6}}{2*-6}=\frac{-48-20\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+20\sqrt{6}}{2*-6}=\frac{-48+20\sqrt{6}}{-12}
$