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2.5(x-8)=0.3(1/5x+4)
We move all terms to the left:
2.5(x-8)-(0.3(1/5x+4))=0
Domain of the equation: 5x+4))!=0We multiply parentheses
x∈R
2.5x-(0.3(1/5x+4))-20=0
We multiply all the terms by the denominator
(2.5x)*5x-20*5x+4))-(0.3(1+4))=0
We add all the numbers together, and all the variables
(+2.5x)*5x-20*5x+4))-(0.35)=0
We add all the numbers together, and all the variables
(+2.5x)*5x-20*5x=0
We multiply parentheses
10x^2-20*5x=0
Wy multiply elements
10x^2-100x=0
a = 10; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·10·0
Δ = 10000
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{10000}=100$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*10}=\frac{0}{20} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*10}=\frac{200}{20} =10 $
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