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X=8X/9X-5
We move all terms to the left:
X-(8X/9X-5)=0
Domain of the equation: 9X-5)!=0We get rid of parentheses
X∈R
X-8X/9X+5=0
We multiply all the terms by the denominator
X*9X-8X+5*9X=0
We add all the numbers together, and all the variables
-8X+X*9X+5*9X=0
Wy multiply elements
9X^2-8X+45X=0
We add all the numbers together, and all the variables
9X^2+37X=0
a = 9; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·9·0
Δ = 1369
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{1369}=37$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*9}=\frac{-74}{18} =-4+1/9 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*9}=\frac{0}{18} =0 $
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