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2/5x+4=-1/6x+8
We move all terms to the left:
2/5x+4-(-1/6x+8)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 6x+8)!=0We get rid of parentheses
x∈R
2/5x+1/6x-8+4=0
We calculate fractions
12x/30x^2+5x/30x^2-8+4=0
We add all the numbers together, and all the variables
12x/30x^2+5x/30x^2-4=0
We multiply all the terms by the denominator
12x+5x-4*30x^2=0
We add all the numbers together, and all the variables
17x-4*30x^2=0
Wy multiply elements
-120x^2+17x=0
a = -120; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-120)·0
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-120}=\frac{-34}{-240} =17/120 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-120}=\frac{0}{-240} =0 $
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