-2-3(x-4)=3/4x+1

Solution for -2-3(x-4)=3/4x+1 equation:

-2-3(x-4)=3/4x+1

We move all terms to the left:

-2-3(x-4)-(3/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We multiply parentheses

-3x-(3/4x+1)+12-2=0

We get rid of parentheses

-3x-3/4x-1+12-2=0

We multiply all the terms by the denominator


-3x*4x-1*4x+12*4x-2*4x-3=0

Wy multiply elements

-12x^2-4x+48x-8x-3=0

We add all the numbers together, and all the variables

-12x^2+36x-3=0

a = -12; b = 36; c = -3;
Δ = b2-4ac
Δ = 362-4·(-12)·(-3)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24\sqrt{2}}{2*-12}=\frac{-36-24\sqrt{2}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24\sqrt{2}}{2*-12}=\frac{-36+24\sqrt{2}}{-24}
$