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1/5x-4=2/7x+5
We move all terms to the left:
1/5x-4-(2/7x+5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 7x+5)!=0We get rid of parentheses
x∈R
1/5x-2/7x-5-4=0
We calculate fractions
7x/35x^2+(-10x)/35x^2-5-4=0
We add all the numbers together, and all the variables
7x/35x^2+(-10x)/35x^2-9=0
We multiply all the terms by the denominator
7x+(-10x)-9*35x^2=0
Wy multiply elements
-315x^2+7x+(-10x)=0
We get rid of parentheses
-315x^2+7x-10x=0
We add all the numbers together, and all the variables
-315x^2-3x=0
a = -315; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-315)·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}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-315}=\frac{0}{-630} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-315}=\frac{6}{-630} =-1/105 $
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