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3/5c+3/10c-6=4
We move all terms to the left:
3/5c+3/10c-6-(4)=0
Domain of the equation: 5c!=0
c!=0/5
c!=0
c∈R
Domain of the equation: 10c!=0We add all the numbers together, and all the variables
c!=0/10
c!=0
c∈R
3/5c+3/10c-10=0
We calculate fractions
30c/50c^2+15c/50c^2-10=0
We multiply all the terms by the denominator
30c+15c-10*50c^2=0
We add all the numbers together, and all the variables
45c-10*50c^2=0
Wy multiply elements
-500c^2+45c=0
a = -500; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-500)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2025}=45$$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-500}=\frac{-90}{-1000} =9/100 $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-500}=\frac{0}{-1000} =0 $
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