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7/5x+5-3/10x+10=11/120
We move all terms to the left:
7/5x+5-3/10x+10-(11/120)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
7/5x-3/10x+5+10-(+11/120)=0
We add all the numbers together, and all the variables
7/5x-3/10x+15-(+11/120)=0
We get rid of parentheses
7/5x-3/10x+15-11/120=0
We calculate fractions
(-550x^2)/6000x^2+8400x/6000x^2+(-1800x)/6000x^2+15=0
We multiply all the terms by the denominator
(-550x^2)+8400x+(-1800x)+15*6000x^2=0
Wy multiply elements
(-550x^2)+90000x^2+8400x+(-1800x)=0
We get rid of parentheses
-550x^2+90000x^2+8400x-1800x=0
We add all the numbers together, and all the variables
89450x^2+6600x=0
a = 89450; b = 6600; c = 0;
Δ = b2-4ac
Δ = 66002-4·89450·0
Δ = 43560000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{43560000}=6600$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6600)-6600}{2*89450}=\frac{-13200}{178900} =-132/1789 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6600)+6600}{2*89450}=\frac{0}{178900} =0 $
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