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2/5y=2.3+3.2y
We move all terms to the left:
2/5y-(2.3+3.2y)=0
Domain of the equation: 5y!=0We add all the numbers together, and all the variables
y!=0/5
y!=0
y∈R
2/5y-(3.2y+2.3)=0
We get rid of parentheses
2/5y-3.2y-2.3=0
We multiply all the terms by the denominator
-(3.2y)*5y-(2.3)*5y+2=0
We add all the numbers together, and all the variables
-(+3.2y)*5y-(2.3)*5y+2=0
We multiply parentheses
-15y^2-11.5y+2=0
a = -15; b = -11.5; c = +2;
Δ = b2-4ac
Δ = -11.52-4·(-15)·2
Δ = 252.25
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11.5)-\sqrt{252.25}}{2*-15}=\frac{11.5-\sqrt{252.25}}{-30} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.5)+\sqrt{252.25}}{2*-15}=\frac{11.5+\sqrt{252.25}}{-30} $
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