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9/10x+x=27
We move all terms to the left:
9/10x+x-(27)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
x+9/10x-27=0
We multiply all the terms by the denominator
x*10x-27*10x+9=0
Wy multiply elements
10x^2-270x+9=0
a = 10; b = -270; c = +9;
Δ = b2-4ac
Δ = -2702-4·10·9
Δ = 72540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72540}=\sqrt{36*2015}=\sqrt{36}*\sqrt{2015}=6\sqrt{2015}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-6\sqrt{2015}}{2*10}=\frac{270-6\sqrt{2015}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+6\sqrt{2015}}{2*10}=\frac{270+6\sqrt{2015}}{20} $
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