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2/5y+8=3/4y+1
We move all terms to the left:
2/5y+8-(3/4y+1)=0
Domain of the equation: 5y!=0
y!=0/5
y!=0
y∈R
Domain of the equation: 4y+1)!=0We get rid of parentheses
y∈R
2/5y-3/4y-1+8=0
We calculate fractions
8y/20y^2+(-15y)/20y^2-1+8=0
We add all the numbers together, and all the variables
8y/20y^2+(-15y)/20y^2+7=0
We multiply all the terms by the denominator
8y+(-15y)+7*20y^2=0
Wy multiply elements
140y^2+8y+(-15y)=0
We get rid of parentheses
140y^2+8y-15y=0
We add all the numbers together, and all the variables
140y^2-7y=0
a = 140; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·140·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*140}=\frac{0}{280} =0 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*140}=\frac{14}{280} =1/20 $
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