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3/5x=19-3/20x-7
We move all terms to the left:
3/5x-(19-3/20x-7)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 20x-7)!=0We add all the numbers together, and all the variables
x∈R
3/5x-(-3/20x+12)=0
We get rid of parentheses
3/5x+3/20x-12=0
We calculate fractions
60x/100x^2+15x/100x^2-12=0
We multiply all the terms by the denominator
60x+15x-12*100x^2=0
We add all the numbers together, and all the variables
75x-12*100x^2=0
Wy multiply elements
-1200x^2+75x=0
a = -1200; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-1200)·0
Δ = 5625
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{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-1200}=\frac{-150}{-2400} =1/16 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-1200}=\frac{0}{-2400} =0 $
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