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6/7x-1/5x=23
We move all terms to the left:
6/7x-1/5x-(23)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 5x!=0We calculate fractions
x!=0/5
x!=0
x∈R
30x/35x^2+(-7x)/35x^2-23=0
We multiply all the terms by the denominator
30x+(-7x)-23*35x^2=0
Wy multiply elements
-805x^2+30x+(-7x)=0
We get rid of parentheses
-805x^2+30x-7x=0
We add all the numbers together, and all the variables
-805x^2+23x=0
a = -805; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-805)·0
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-805}=\frac{-46}{-1610} =1/35 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-805}=\frac{0}{-1610} =0 $
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