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3/5x+3/10x=28/15
We move all terms to the left:
3/5x+3/10x-(28/15)=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
3/5x+3/10x-(+28/15)=0
We get rid of parentheses
3/5x+3/10x-28/15=0
We calculate fractions
(-1400x^2)/750x^2+450x/750x^2+225x/750x^2=0
We multiply all the terms by the denominator
(-1400x^2)+450x+225x=0
We add all the numbers together, and all the variables
(-1400x^2)+675x=0
We get rid of parentheses
-1400x^2+675x=0
a = -1400; b = 675; c = 0;
Δ = b2-4ac
Δ = 6752-4·(-1400)·0
Δ = 455625
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{455625}=675$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(675)-675}{2*-1400}=\frac{-1350}{-2800} =27/56 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(675)+675}{2*-1400}=\frac{0}{-2800} =0 $
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