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2/5x-2=7/10x-14
We move all terms to the left:
2/5x-2-(7/10x-14)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x-14)!=0We get rid of parentheses
x∈R
2/5x-7/10x+14-2=0
We calculate fractions
20x/50x^2+(-35x)/50x^2+14-2=0
We add all the numbers together, and all the variables
20x/50x^2+(-35x)/50x^2+12=0
We multiply all the terms by the denominator
20x+(-35x)+12*50x^2=0
Wy multiply elements
600x^2+20x+(-35x)=0
We get rid of parentheses
600x^2+20x-35x=0
We add all the numbers together, and all the variables
600x^2-15x=0
a = 600; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·600·0
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*600}=\frac{0}{1200} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*600}=\frac{30}{1200} =1/40 $
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