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1/2x+x=7
We move all terms to the left:
1/2x+x-(7)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
x+1/2x-7=0
We multiply all the terms by the denominator
x*2x-7*2x+1=0
Wy multiply elements
2x^2-14x+1=0
a = 2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·2·1
Δ = 188
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*2}=\frac{14-2\sqrt{47}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*2}=\frac{14+2\sqrt{47}}{4} $
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