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2/3x-1/6=2/5x+6
We move all terms to the left:
2/3x-1/6-(2/5x+6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x+6)!=0We get rid of parentheses
x∈R
2/3x-2/5x-6-1/6=0
We calculate fractions
(-75x^2)/540x^2+360x/540x^2+(-216x)/540x^2-6=0
We multiply all the terms by the denominator
(-75x^2)+360x+(-216x)-6*540x^2=0
Wy multiply elements
(-75x^2)-3240x^2+360x+(-216x)=0
We get rid of parentheses
-75x^2-3240x^2+360x-216x=0
We add all the numbers together, and all the variables
-3315x^2+144x=0
a = -3315; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-3315)·0
Δ = 20736
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{20736}=144$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-3315}=\frac{-288}{-6630} =48/1105 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-3315}=\frac{0}{-6630} =0 $
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