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3/2x+7/10=1/5x+2
We move all terms to the left:
3/2x+7/10-(1/5x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x+2)!=0We get rid of parentheses
x∈R
3/2x-1/5x-2+7/10=0
We calculate fractions
350x^2/100x^2+150x/100x^2+(-20x)/100x^2-2=0
We multiply all the terms by the denominator
350x^2+150x+(-20x)-2*100x^2=0
Wy multiply elements
350x^2-200x^2+150x+(-20x)=0
We get rid of parentheses
350x^2-200x^2+150x-20x=0
We add all the numbers together, and all the variables
150x^2+130x=0
a = 150; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·150·0
Δ = 16900
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{16900}=130$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*150}=\frac{-260}{300} =-13/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*150}=\frac{0}{300} =0 $
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