5x2-4x=1

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Solution for 5x2-4x=1 equation:



5x^2-4x=1
We move all terms to the left:
5x^2-4x-(1)=0
a = 5; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·5·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*5}=\frac{-2}{10} =-1/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*5}=\frac{10}{10} =1 $

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