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3/10x+7=4/5x
We move all terms to the left:
3/10x+7-(4/5x)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 5x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/10x-(+4/5x)+7=0
We get rid of parentheses
3/10x-4/5x+7=0
We calculate fractions
15x/50x^2+(-40x)/50x^2+7=0
We multiply all the terms by the denominator
15x+(-40x)+7*50x^2=0
Wy multiply elements
350x^2+15x+(-40x)=0
We get rid of parentheses
350x^2+15x-40x=0
We add all the numbers together, and all the variables
350x^2-25x=0
a = 350; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·350·0
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*350}=\frac{0}{700} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*350}=\frac{50}{700} =1/14 $
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