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4y/5y-3y=-33
We move all terms to the left:
4y/5y-3y-(-33)=0
Domain of the equation: 5y!=0We add all the numbers together, and all the variables
y!=0/5
y!=0
y∈R
-3y+4y/5y+33=0
We multiply all the terms by the denominator
-3y*5y+4y+33*5y=0
We add all the numbers together, and all the variables
4y-3y*5y+33*5y=0
Wy multiply elements
-15y^2+4y+165y=0
We add all the numbers together, and all the variables
-15y^2+169y=0
a = -15; b = 169; c = 0;
Δ = b2-4ac
Δ = 1692-4·(-15)·0
Δ = 28561
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{28561}=169$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(169)-169}{2*-15}=\frac{-338}{-30} =11+4/15 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(169)+169}{2*-15}=\frac{0}{-30} =0 $
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