3/4x-6=-4x+6

Solution for 3/4x-6=-4x+6 equation:

3/4x-6=-4x+6

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x+4x-6-6=0

We multiply all the terms by the denominator


4x*4x-6*4x-6*4x+3=0

Wy multiply elements

16x^2-24x-24x+3=0

We add all the numbers together, and all the variables

16x^2-48x+3=0

a = 16; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·16·3
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{33}}{2*16}=\frac{48-8\sqrt{33}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{33}}{2*16}=\frac{48+8\sqrt{33}}{32}
$