7/9x-6=4.5x=

Solution for 7/9x-6=4.5x= equation:

7/9x-6=4.5x=

We move all terms to the left:

7/9x-6-(4.5x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

7/9x-(+4.5x)-6=0

We get rid of parentheses

7/9x-4.5x-6=0

We multiply all the terms by the denominator


-(4.5x)*9x-6*9x+7=0

We add all the numbers together, and all the variables

-(+4.5x)*9x-6*9x+7=0

We multiply parentheses

-36x^2-6*9x+7=0

Wy multiply elements

-36x^2-54x+7=0

a = -36; b = -54; c = +7;
Δ = b2-4ac
Δ = -542-4·(-36)·7
Δ = 3924
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:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{109}}{2*-36}=\frac{54-6\sqrt{109}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{109}}{2*-36}=\frac{54+6\sqrt{109}}{-72}
$