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2+1/10x+x=90
We move all terms to the left:
2+1/10x+x-(90)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
x+1/10x-88=0
We multiply all the terms by the denominator
x*10x-88*10x+1=0
Wy multiply elements
10x^2-880x+1=0
a = 10; b = -880; c = +1;
Δ = b2-4ac
Δ = -8802-4·10·1
Δ = 774360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{774360}=\sqrt{324*2390}=\sqrt{324}*\sqrt{2390}=18\sqrt{2390}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-18\sqrt{2390}}{2*10}=\frac{880-18\sqrt{2390}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+18\sqrt{2390}}{2*10}=\frac{880+18\sqrt{2390}}{20} $
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