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6/3+4/2x=0.5x+17
We move all terms to the left:
6/3+4/2x-(0.5x+17)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
4/2x-(0.5x+17)+2=0
We get rid of parentheses
4/2x-0.5x-17+2=0
We multiply all the terms by the denominator
-(0.5x)*2x-17*2x+2*2x+4=0
We add all the numbers together, and all the variables
-(+0.5x)*2x-17*2x+2*2x+4=0
We multiply parentheses
-0x^2-17*2x+2*2x+4=0
Wy multiply elements
-0x^2-34x+4x+4=0
We add all the numbers together, and all the variables
-1x^2-30x+4=0
a = -1; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·(-1)·4
Δ = 916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*-1}=\frac{30-2\sqrt{229}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*-1}=\frac{30+2\sqrt{229}}{-2} $
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