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1/5x-7=1/4x+3
We move all terms to the left:
1/5x-7-(1/4x+3)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x+3)!=0We get rid of parentheses
x∈R
1/5x-1/4x-3-7=0
We calculate fractions
4x/20x^2+(-5x)/20x^2-3-7=0
We add all the numbers together, and all the variables
4x/20x^2+(-5x)/20x^2-10=0
We multiply all the terms by the denominator
4x+(-5x)-10*20x^2=0
Wy multiply elements
-200x^2+4x+(-5x)=0
We get rid of parentheses
-200x^2+4x-5x=0
We add all the numbers together, and all the variables
-200x^2-1x=0
a = -200; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-200)·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-200}=\frac{0}{-400} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-200}=\frac{2}{-400} =-1/200 $
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