3x-11/4x=-2

Solution for 3x-11/4x=-2 equation:

3x-11/4x=-2

We move all terms to the left:

3x-11/4x-(-2)=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-11/4x+2=0

We multiply all the terms by the denominator


3x*4x+2*4x-11=0

Wy multiply elements

12x^2+8x-11=0

a = 12; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·12·(-11)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{37}}{2*12}=\frac{-8-4\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{37}}{2*12}=\frac{-8+4\sqrt{37}}{24}
$