2.25y-12=1/4y-4

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Solution for 2.25y-12=1/4y-4 equation:



2.25y-12=1/4y-4
We move all terms to the left:
2.25y-12-(1/4y-4)=0
Domain of the equation: 4y-4)!=0
y∈R
We get rid of parentheses
2.25y-1/4y+4-12=0
We multiply all the terms by the denominator
(2.25y)*4y+4*4y-12*4y-1=0
We add all the numbers together, and all the variables
(+2.25y)*4y+4*4y-12*4y-1=0
We multiply parentheses
8y^2+4*4y-12*4y-1=0
Wy multiply elements
8y^2+16y-48y-1=0
We add all the numbers together, and all the variables
8y^2-32y-1=0
a = 8; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·8·(-1)
Δ = 1056
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:
$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*8}=\frac{32-4\sqrt{66}}{16} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*8}=\frac{32+4\sqrt{66}}{16} $

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