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4+x=-1/2x=-1+1/2
We move all terms to the left:
4+x-(-1/2x)=0
Domain of the equation: 2x)!=0We get rid of parentheses
x!=0/1
x!=0
x∈R
x+1/2x+4=0
We multiply all the terms by the denominator
x*2x+4*2x+1=0
Wy multiply elements
2x^2+8x+1=0
a = 2; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·2·1
Δ = 56
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*2}=\frac{-8-2\sqrt{14}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*2}=\frac{-8+2\sqrt{14}}{4} $
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