2(3-6x)-9=3/4x+8

Solution for 2(3-6x)-9=3/4x+8 equation:

2(3-6x)-9=3/4x+8

We move all terms to the left:

2(3-6x)-9-(3/4x+8)=0


Domain of the equation: 4x+8)!=0

x∈R


We add all the numbers together, and all the variables

2(-6x+3)-(3/4x+8)-9=0

We multiply parentheses

-12x-(3/4x+8)+6-9=0

We get rid of parentheses

-12x-3/4x-8+6-9=0

We multiply all the terms by the denominator


-12x*4x-8*4x+6*4x-9*4x-3=0

Wy multiply elements

-48x^2-32x+24x-36x-3=0

We add all the numbers together, and all the variables

-48x^2-44x-3=0

a = -48; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·(-48)·(-3)
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{85}}{2*-48}=\frac{44-4\sqrt{85}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{85}}{2*-48}=\frac{44+4\sqrt{85}}{-96}
$