6x+4x-6=24/9x

Solution for 6x+4x-6=24/9x equation:

6x+4x-6=24/9x

We move all terms to the left:

6x+4x-6-(24/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x+4x-(+24/9x)-6=0

We add all the numbers together, and all the variables

10x-(+24/9x)-6=0

We get rid of parentheses

10x-24/9x-6=0

We multiply all the terms by the denominator


10x*9x-6*9x-24=0

Wy multiply elements

90x^2-54x-24=0

a = 90; b = -54; c = -24;
Δ = b2-4ac
Δ = -542-4·90·(-24)
Δ = 11556
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:

$\sqrt{\Delta}=\sqrt{11556}=\sqrt{36*321}=\sqrt{36}*\sqrt{321}=6\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{321}}{2*90}=\frac{54-6\sqrt{321}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{321}}{2*90}=\frac{54+6\sqrt{321}}{180}
$