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3/5x-3/2x=10
We move all terms to the left:
3/5x-3/2x-(10)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x!=0We calculate fractions
x!=0/2
x!=0
x∈R
6x/10x^2+(-15x)/10x^2-10=0
We multiply all the terms by the denominator
6x+(-15x)-10*10x^2=0
Wy multiply elements
-100x^2+6x+(-15x)=0
We get rid of parentheses
-100x^2+6x-15x=0
We add all the numbers together, and all the variables
-100x^2-9x=0
a = -100; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-100)·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-100}=\frac{0}{-200} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-100}=\frac{18}{-200} =-9/100 $
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