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7/10x+8=3/5x
We move all terms to the left:
7/10x+8-(3/5x)=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
7/10x-(+3/5x)+8=0
We get rid of parentheses
7/10x-3/5x+8=0
We calculate fractions
35x/50x^2+(-30x)/50x^2+8=0
We multiply all the terms by the denominator
35x+(-30x)+8*50x^2=0
Wy multiply elements
400x^2+35x+(-30x)=0
We get rid of parentheses
400x^2+35x-30x=0
We add all the numbers together, and all the variables
400x^2+5x=0
a = 400; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·400·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*400}=\frac{-10}{800} =-1/80 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*400}=\frac{0}{800} =0 $
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