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4y+4/y=21
We move all terms to the left:
4y+4/y-(21)=0
Domain of the equation: y!=0We multiply all the terms by the denominator
y∈R
4y*y-21*y+4=0
We add all the numbers together, and all the variables
-21y+4y*y+4=0
Wy multiply elements
4y^2-21y+4=0
a = 4; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·4·4
Δ = 377
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{-(-21)-\sqrt{377}}{2*4}=\frac{21-\sqrt{377}}{8} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{377}}{2*4}=\frac{21+\sqrt{377}}{8} $
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