3/4x+2=3x-1

Solution for 3/4x+2=3x-1 equation:

3/4x+2=3x-1

We move all terms to the left:

3/4x+2-(3x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-3x+1+2=0

We multiply all the terms by the denominator


-3x*4x+1*4x+2*4x+3=0

Wy multiply elements

-12x^2+4x+8x+3=0

We add all the numbers together, and all the variables

-12x^2+12x+3=0

a = -12; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-12)·3
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-12}=\frac{-12-12\sqrt{2}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-12}=\frac{-12+12\sqrt{2}}{-24}
$