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6/5x-7/5=1/3x-7
We move all terms to the left:
6/5x-7/5-(1/3x-7)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x-7)!=0We get rid of parentheses
x∈R
6/5x-1/3x+7-7/5=0
We calculate fractions
18x/375x^2+(-125x)/375x^2+(-21x)/375x^2+7=0
We multiply all the terms by the denominator
18x+(-125x)+(-21x)+7*375x^2=0
Wy multiply elements
2625x^2+18x+(-125x)+(-21x)=0
We get rid of parentheses
2625x^2+18x-125x-21x=0
We add all the numbers together, and all the variables
2625x^2-128x=0
a = 2625; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·2625·0
Δ = 16384
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{16384}=128$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*2625}=\frac{0}{5250} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*2625}=\frac{256}{5250} =128/2625 $
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