5y2-8y=2

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Solution for 5y2-8y=2 equation:



5y^2-8y=2
We move all terms to the left:
5y^2-8y-(2)=0
a = 5; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·5·(-2)
Δ = 104
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:
$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*5}=\frac{8-2\sqrt{26}}{10} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*5}=\frac{8+2\sqrt{26}}{10} $

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