24-3(6-3x)=11/4x

Solution for 24-3(6-3x)=11/4x equation:

24-3(6-3x)=11/4x

We move all terms to the left:

24-3(6-3x)-(11/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3(-3x+6)-(+11/4x)+24=0

We multiply parentheses

9x-(+11/4x)-18+24=0

We get rid of parentheses

9x-11/4x-18+24=0

We multiply all the terms by the denominator


9x*4x-18*4x+24*4x-11=0

Wy multiply elements

36x^2-72x+96x-11=0

We add all the numbers together, and all the variables

36x^2+24x-11=0

a = 36; b = 24; c = -11;
Δ = b2-4ac
Δ = 242-4·36·(-11)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{15}}{2*36}=\frac{-24-12\sqrt{15}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{15}}{2*36}=\frac{-24+12\sqrt{15}}{72}
$