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6/10x-1.5=8.9+0.2x
We move all terms to the left:
6/10x-1.5-(8.9+0.2x)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
6/10x-(0.2x+8.9)-1.5=0
We get rid of parentheses
6/10x-0.2x-8.9-1.5=0
We multiply all the terms by the denominator
-(0.2x)*10x-(8.9)*10x-(1.5)*10x+6=0
We add all the numbers together, and all the variables
-(+0.2x)*10x-(8.9)*10x-(1.5)*10x+6=0
We multiply parentheses
-0x^2-89x-15x+6=0
We add all the numbers together, and all the variables
-1x^2-104x+6=0
a = -1; b = -104; c = +6;
Δ = b2-4ac
Δ = -1042-4·(-1)·6
Δ = 10840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10840}=\sqrt{4*2710}=\sqrt{4}*\sqrt{2710}=2\sqrt{2710}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-2\sqrt{2710}}{2*-1}=\frac{104-2\sqrt{2710}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+2\sqrt{2710}}{2*-1}=\frac{104+2\sqrt{2710}}{-2} $
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