3/4x+2=4x-2

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

3/4x+2=4x-2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -16; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-16)·3
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{7}}{2*-16}=\frac{-16-8\sqrt{7}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{7}}{2*-16}=\frac{-16+8\sqrt{7}}{-32}
$