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-3/5x-7/10x+1/2=-56
We move all terms to the left:
-3/5x-7/10x+1/2-(-56)=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
-3/5x-7/10x+56+1/2=0
We calculate fractions
50x^2/200x^2+(-120x)/200x^2+(-140x)/200x^2+56=0
We multiply all the terms by the denominator
50x^2+(-120x)+(-140x)+56*200x^2=0
Wy multiply elements
50x^2+11200x^2+(-120x)+(-140x)=0
We get rid of parentheses
50x^2+11200x^2-120x-140x=0
We add all the numbers together, and all the variables
11250x^2-260x=0
a = 11250; b = -260; c = 0;
Δ = b2-4ac
Δ = -2602-4·11250·0
Δ = 67600
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{67600}=260$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-260}{2*11250}=\frac{0}{22500} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+260}{2*11250}=\frac{520}{22500} =26/1125 $
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