3x+2/4x=18

Solution for 3x+2/4x=18 equation:

3x+2/4x=18

We move all terms to the left:

3x+2/4x-(18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


3x*4x-18*4x+2=0

Wy multiply elements

12x^2-72x+2=0

a = 12; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·12·2
Δ = 5088
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:

$\sqrt{\Delta}=\sqrt{5088}=\sqrt{16*318}=\sqrt{16}*\sqrt{318}=4\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{318}}{2*12}=\frac{72-4\sqrt{318}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{318}}{2*12}=\frac{72+4\sqrt{318}}{24}
$