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X=6-5X/6X
We move all terms to the left:
X-(6-5X/6X)=0
Domain of the equation: 6X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(-5X/6X+6)=0
We get rid of parentheses
X+5X/6X-6=0
We multiply all the terms by the denominator
X*6X+5X-6*6X=0
We add all the numbers together, and all the variables
5X+X*6X-6*6X=0
Wy multiply elements
6X^2+5X-36X=0
We add all the numbers together, and all the variables
6X^2-31X=0
a = 6; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·6·0
Δ = 961
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{961}=31$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*6}=\frac{0}{12} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*6}=\frac{62}{12} =5+1/6 $
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