2-2y=3/4y+13

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Solution for 2-2y=3/4y+13 equation:



2-2y=3/4y+13
We move all terms to the left:
2-2y-(3/4y+13)=0
Domain of the equation: 4y+13)!=0
y∈R
We get rid of parentheses
-2y-3/4y-13+2=0
We multiply all the terms by the denominator
-2y*4y-13*4y+2*4y-3=0
Wy multiply elements
-8y^2-52y+8y-3=0
We add all the numbers together, and all the variables
-8y^2-44y-3=0
a = -8; b = -44; c = -3;
Δ = b2-4ac
Δ = -442-4·(-8)·(-3)
Δ = 1840
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:
$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{115}}{2*-8}=\frac{44-4\sqrt{115}}{-16} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{115}}{2*-8}=\frac{44+4\sqrt{115}}{-16} $

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