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X=1/10X+2
We move all terms to the left:
X-(1/10X+2)=0
Domain of the equation: 10X+2)!=0We get rid of parentheses
X∈R
X-1/10X-2=0
We multiply all the terms by the denominator
X*10X-2*10X-1=0
Wy multiply elements
10X^2-20X-1=0
a = 10; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·10·(-1)
Δ = 440
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*10}=\frac{20-2\sqrt{110}}{20} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*10}=\frac{20+2\sqrt{110}}{20} $
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