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4/5x+2/10x-9/9=-11/16
We move all terms to the left:
4/5x+2/10x-9/9-(-11/16)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
4/5x+2/10x-1-(-11/16)=0
We get rid of parentheses
4/5x+2/10x-1+11/16=0
We calculate fractions
550x^2/800x^2+640x/800x^2+160x/800x^2-1=0
We multiply all the terms by the denominator
550x^2+640x+160x-1*800x^2=0
We add all the numbers together, and all the variables
550x^2+800x-1*800x^2=0
Wy multiply elements
550x^2-800x^2+800x=0
We add all the numbers together, and all the variables
-250x^2+800x=0
a = -250; b = 800; c = 0;
Δ = b2-4ac
Δ = 8002-4·(-250)·0
Δ = 640000
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{640000}=800$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(800)-800}{2*-250}=\frac{-1600}{-500} =3+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(800)+800}{2*-250}=\frac{0}{-500} =0 $
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