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3/2x+2=4/5x+8
We move all terms to the left:
3/2x+2-(4/5x+8)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x+8)!=0We get rid of parentheses
x∈R
3/2x-4/5x-8+2=0
We calculate fractions
15x/10x^2+(-8x)/10x^2-8+2=0
We add all the numbers together, and all the variables
15x/10x^2+(-8x)/10x^2-6=0
We multiply all the terms by the denominator
15x+(-8x)-6*10x^2=0
Wy multiply elements
-60x^2+15x+(-8x)=0
We get rid of parentheses
-60x^2+15x-8x=0
We add all the numbers together, and all the variables
-60x^2+7x=0
a = -60; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-60)·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-60}=\frac{-14}{-120} =7/60 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-60}=\frac{0}{-120} =0 $
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