8y(8+3y)/4+9y=77

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Solution for 8y(8+3y)/4+9y=77 equation:



8y(8+3y)/4+9y=77
We move all terms to the left:
8y(8+3y)/4+9y-(77)=0
We add all the numbers together, and all the variables
8y(3y+8)/4+9y-77=0
We add all the numbers together, and all the variables
9y+8y(3y+8)/4-77=0
We multiply all the terms by the denominator
9y*4+8y(3y+8)-77*4=0
We add all the numbers together, and all the variables
9y*4+8y(3y+8)-308=0
We multiply parentheses
24y^2+9y*4+64y-308=0
Wy multiply elements
24y^2+36y+64y-308=0
We add all the numbers together, and all the variables
24y^2+100y-308=0
a = 24; b = 100; c = -308;
Δ = b2-4ac
Δ = 1002-4·24·(-308)
Δ = 39568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{39568}=\sqrt{16*2473}=\sqrt{16}*\sqrt{2473}=4\sqrt{2473}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{2473}}{2*24}=\frac{-100-4\sqrt{2473}}{48} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{2473}}{2*24}=\frac{-100+4\sqrt{2473}}{48} $

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