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5y-51.25=-3+3/4y
We move all terms to the left:
5y-51.25-(-3+3/4y)=0
Domain of the equation: 4y)!=0We add all the numbers together, and all the variables
y!=0/1
y!=0
y∈R
5y-(3/4y-3)-51.25=0
We get rid of parentheses
5y-3/4y+3-51.25=0
We multiply all the terms by the denominator
5y*4y+3*4y-(51.25)*4y-3=0
We multiply parentheses
5y*4y+3*4y-205y-3=0
Wy multiply elements
20y^2+12y-205y-3=0
We add all the numbers together, and all the variables
20y^2-193y-3=0
a = 20; b = -193; c = -3;
Δ = b2-4ac
Δ = -1932-4·20·(-3)
Δ = 37489
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{-(-193)-\sqrt{37489}}{2*20}=\frac{193-\sqrt{37489}}{40} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-193)+\sqrt{37489}}{2*20}=\frac{193+\sqrt{37489}}{40} $
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