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3/10x-1/10x=1/2x+1
We move all terms to the left:
3/10x-1/10x-(1/2x+1)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
Domain of the equation: 2x+1)!=0We get rid of parentheses
x∈R
3/10x-1/10x-1/2x-1=0
We calculate fractions
(-2x+3)/20x^2+(-10x)/20x^2-1=0
We multiply all the terms by the denominator
(-2x+3)+(-10x)-1*20x^2=0
Wy multiply elements
-20x^2+(-2x+3)+(-10x)=0
We get rid of parentheses
-20x^2-2x-10x+3=0
We add all the numbers together, and all the variables
-20x^2-12x+3=0
a = -20; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-20)·3
Δ = 384
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{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*-20}=\frac{12-8\sqrt{6}}{-40}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*-20}=\frac{12+8\sqrt{6}}{-40}
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