1.1+3/4x+2=3.1+3.4x

Solution for 1.1+3/4x+2=3.1+3.4x equation:

1.1+3/4x+2=3.1+3.4x

We move all terms to the left:

1.1+3/4x+2-(3.1+3.4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(3.4x+3.1)+1.1+2=0

We add all the numbers together, and all the variables

3/4x-(3.4x+3.1)+3.1=0

We get rid of parentheses

3/4x-3.4x-3.1+3.1=0

We multiply all the terms by the denominator


-(3.4x)*4x-(3.1)*4x+(3.1)*4x+3=0

We add all the numbers together, and all the variables

-(+3.4x)*4x-(3.1)*4x+(3.1)*4x+3=0

We multiply parentheses

-12x^2-12.4x+12.4x+3=0

We add all the numbers together, and all the variables

-12x^2+3=0

a = -12; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-12)·3
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-12}=\frac{-12}{-24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-12}=\frac{12}{-24}
=-1/2
$