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1/5x-1/2x=6
We move all terms to the left:
1/5x-1/2x-(6)=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
2x/10x^2+(-5x)/10x^2-6=0
We multiply all the terms by the denominator
2x+(-5x)-6*10x^2=0
Wy multiply elements
-60x^2+2x+(-5x)=0
We get rid of parentheses
-60x^2+2x-5x=0
We add all the numbers together, and all the variables
-60x^2-3x=0
a = -60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-60)·0
Δ = 9
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{9}=3x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-60}=\frac{0}{-120} =0x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-60}=\frac{6}{-120} =-1/20
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