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7/10x-2=2/5x+1
We move all terms to the left:
7/10x-2-(2/5x+1)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 5x+1)!=0We get rid of parentheses
x∈R
7/10x-2/5x-1-2=0
We calculate fractions
35x/50x^2+(-20x)/50x^2-1-2=0
We add all the numbers together, and all the variables
35x/50x^2+(-20x)/50x^2-3=0
We multiply all the terms by the denominator
35x+(-20x)-3*50x^2=0
Wy multiply elements
-150x^2+35x+(-20x)=0
We get rid of parentheses
-150x^2+35x-20x=0
We add all the numbers together, and all the variables
-150x^2+15x=0
a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-150}=\frac{-30}{-300} =1/10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300} =0 $
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