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5/7x-5=5/6x+7
We move all terms to the left:
5/7x-5-(5/6x+7)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 6x+7)!=0We get rid of parentheses
x∈R
5/7x-5/6x-7-5=0
We calculate fractions
30x/42x^2+(-35x)/42x^2-7-5=0
We add all the numbers together, and all the variables
30x/42x^2+(-35x)/42x^2-12=0
We multiply all the terms by the denominator
30x+(-35x)-12*42x^2=0
Wy multiply elements
-504x^2+30x+(-35x)=0
We get rid of parentheses
-504x^2+30x-35x=0
We add all the numbers together, and all the variables
-504x^2-5x=0
a = -504; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-504)·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-504}=\frac{0}{-1008} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-504}=\frac{10}{-1008} =-5/504 $
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