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X+5-(1/2X)=17
We move all terms to the left:
X+5-(1/2X)-(17)=0
Domain of the equation: 2X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(+1/2X)+5-17=0
We add all the numbers together, and all the variables
X-(+1/2X)-12=0
We get rid of parentheses
X-1/2X-12=0
We multiply all the terms by the denominator
X*2X-12*2X-1=0
Wy multiply elements
2X^2-24X-1=0
a = 2; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·2·(-1)
Δ = 584
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{146}}{2*2}=\frac{24-2\sqrt{146}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{146}}{2*2}=\frac{24+2\sqrt{146}}{4} $
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