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6x+9x/4x+6x=8/27
We move all terms to the left:
6x+9x/4x+6x-(8/27)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
6x+9x/4x+6x-(+8/27)=0
We add all the numbers together, and all the variables
12x+9x/4x-(+8/27)=0
We get rid of parentheses
12x+9x/4x-8/27=0
We calculate fractions
12x+243x/108x+(-32x)/108x=0
We multiply all the terms by the denominator
12x*108x+243x+(-32x)=0
We add all the numbers together, and all the variables
243x+12x*108x+(-32x)=0
Wy multiply elements
1296x^2+243x+(-32x)=0
We get rid of parentheses
1296x^2+243x-32x=0
We add all the numbers together, and all the variables
1296x^2+211x=0
a = 1296; b = 211; c = 0;
Δ = b2-4ac
Δ = 2112-4·1296·0
Δ = 44521
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{44521}=211$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(211)-211}{2*1296}=\frac{-422}{2592} =-211/1296 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(211)+211}{2*1296}=\frac{0}{2592} =0 $
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