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6/15x+8=5/7x-2
We move all terms to the left:
6/15x+8-(5/7x-2)=0
Domain of the equation: 15x!=0
x!=0/15
x!=0
x∈R
Domain of the equation: 7x-2)!=0We get rid of parentheses
x∈R
6/15x-5/7x+2+8=0
We calculate fractions
42x/105x^2+(-75x)/105x^2+2+8=0
We add all the numbers together, and all the variables
42x/105x^2+(-75x)/105x^2+10=0
We multiply all the terms by the denominator
42x+(-75x)+10*105x^2=0
Wy multiply elements
1050x^2+42x+(-75x)=0
We get rid of parentheses
1050x^2+42x-75x=0
We add all the numbers together, and all the variables
1050x^2-33x=0
a = 1050; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·1050·0
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*1050}=\frac{0}{2100} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*1050}=\frac{66}{2100} =11/350 $
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