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(3x-18)6=x/5x=
We move all terms to the left:
(3x-18)6-(x/5x)=0
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(3x-18)6-(+x/5x)=0
We multiply parentheses
18x-(+x/5x)-108=0
We get rid of parentheses
18x-x/5x-108=0
We multiply all the terms by the denominator
18x*5x-x-108*5x=0
We add all the numbers together, and all the variables
-1x+18x*5x-108*5x=0
Wy multiply elements
90x^2-1x-540x=0
We add all the numbers together, and all the variables
90x^2-541x=0
a = 90; b = -541; c = 0;
Δ = b2-4ac
Δ = -5412-4·90·0
Δ = 292681
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{292681}=541$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-541)-541}{2*90}=\frac{0}{180} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-541)+541}{2*90}=\frac{1082}{180} =6+1/90 $
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