3/4x+2-3x=6

Solution for 3/4x+2-3x=6 equation:

3/4x+2-3x=6

We move all terms to the left:

3/4x+2-3x-(6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -12; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·(-12)·3
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*-12}=\frac{-4}{-24}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*-12}=\frac{36}{-24}
=-1+1/2
$