3x-4=3/4x+2

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

3x-4=3/4x+2

We move all terms to the left:

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


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-8x-16x-3=0

We add all the numbers together, and all the variables

12x^2-24x-3=0

a = 12; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·12·(-3)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*12}=\frac{24-12\sqrt{5}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*12}=\frac{24+12\sqrt{5}}{24}
$