2x-1=3/4x*9

Solution for 2x-1=3/4x*9 equation:

2x-1=3/4x*9

We move all terms to the left:

2x-1-(3/4x*9)=0


Domain of the equation: 4x*9)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+3/4x*9)-1=0

We get rid of parentheses

2x-3/4x*9-1=0

We multiply all the terms by the denominator


2x*4x*9-1*4x*9-3=0

Wy multiply elements

72x^2*9-36x*9-3=0

Wy multiply elements

648x^2-324x-3=0

a = 648; b = -324; c = -3;
Δ = b2-4ac
Δ = -3242-4·648·(-3)
Δ = 112752
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:

$\sqrt{\Delta}=\sqrt{112752}=\sqrt{1296*87}=\sqrt{1296}*\sqrt{87}=36\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-36\sqrt{87}}{2*648}=\frac{324-36\sqrt{87}}{1296}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+36\sqrt{87}}{2*648}=\frac{324+36\sqrt{87}}{1296}
$