-3/4x-8=-x+4

Solution for -3/4x-8=-x+4 equation:

-3/4x-8=-x+4

We move all terms to the left:

-3/4x-8-(-x+4)=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-(-1x+4)-8=0

We get rid of parentheses

-3/4x+1x-4-8=0

We multiply all the terms by the denominator


1x*4x-4*4x-8*4x-3=0

Wy multiply elements

4x^2-16x-32x-3=0

We add all the numbers together, and all the variables

4x^2-48x-3=0

a = 4; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·4·(-3)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*4}=\frac{48-28\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*4}=\frac{48+28\sqrt{3}}{8}
$