4y2-40y=100

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Solution for 4y2-40y=100 equation:



4y^2-40y=100
We move all terms to the left:
4y^2-40y-(100)=0
a = 4; b = -40; c = -100;
Δ = b2-4ac
Δ = -402-4·4·(-100)
Δ = 3200
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:
$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{2}}{2*4}=\frac{40-40\sqrt{2}}{8} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{2}}{2*4}=\frac{40+40\sqrt{2}}{8} $

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