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4(x-2)-(1/5)(20x+5)=32
We move all terms to the left:
4(x-2)-(1/5)(20x+5)-(32)=0
Domain of the equation: 5)(20x+5)!=0We add all the numbers together, and all the variables
x∈R
4(x-2)-(+1/5)(20x+5)-32=0
We multiply parentheses
4x-(+1/5)(20x+5)-8-32=0
We multiply parentheses ..
-(+20x^2+1/5*5)+4x-8-32=0
We multiply all the terms by the denominator
-(+20x^2+1+4x*5*5)-8*5*5)-32*5*5)=0
We add all the numbers together, and all the variables
-(+20x^2+1+4x*5*5)=0
We get rid of parentheses
-20x^2-4x*5*5-1=0
Wy multiply elements
-20x^2-100x*5-1=0
Wy multiply elements
-20x^2-500x-1=0
a = -20; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·(-20)·(-1)
Δ = 249920
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}
The end solution:
\sqrt{\Delta}=\sqrt{249920}=\sqrt{64*3905}=\sqrt{64}*\sqrt{3905}=8\sqrt{3905}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-8\sqrt{3905}}{2*-20}=\frac{500-8\sqrt{3905}}{-40}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+8\sqrt{3905}}{2*-20}=\frac{500+8\sqrt{3905}}{-40}
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