3/4x-18=2x

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

3/4x-18=2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-72x+3=0

a = -8; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·(-8)·3
Δ = 5280
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:

$\sqrt{\Delta}=\sqrt{5280}=\sqrt{16*330}=\sqrt{16}*\sqrt{330}=4\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{330}}{2*-8}=\frac{72-4\sqrt{330}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{330}}{2*-8}=\frac{72+4\sqrt{330}}{-16}
$