Y=x2-5x+4

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Solution for Y=x2-5x+4 equation:



=Y2-5Y+4
We move all terms to the left:
-(Y2-5Y+4)=0
We add all the numbers together, and all the variables
-(+Y^2-5Y+4)=0
We get rid of parentheses
-Y^2+5Y-4=0
We add all the numbers together, and all the variables
-1Y^2+5Y-4=0
a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2} =+4 $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2} =1 $

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