3/4x=9-18x

Solution for 3/4x=9-18x equation:

3/4x=9-18x

We move all terms to the left:

3/4x-(9-18x)=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-(-18x+9)=0

We get rid of parentheses

3/4x+18x-9=0

We multiply all the terms by the denominator


18x*4x-9*4x+3=0

Wy multiply elements

72x^2-36x+3=0

a = 72; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·72·3
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{3}}{2*72}=\frac{36-12\sqrt{3}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{3}}{2*72}=\frac{36+12\sqrt{3}}{144}
$