-3/4*x-4=5+2x

Solution for -3/4*x-4=5+2x equation:

-3/4x-4=5+2x

We move all terms to the left:

-3/4x-4-(5+2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(2x+5)-4=0

We get rid of parentheses

-3/4x-2x-5-4=0

We multiply all the terms by the denominator


-2x*4x-5*4x-4*4x-3=0

Wy multiply elements

-8x^2-20x-16x-3=0

We add all the numbers together, and all the variables

-8x^2-36x-3=0

a = -8; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·(-8)·(-3)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20\sqrt{3}}{2*-8}=\frac{36-20\sqrt{3}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20\sqrt{3}}{2*-8}=\frac{36+20\sqrt{3}}{-16}
$