Y=x2-7x+3

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Solution for Y=x2-7x+3 equation:



=Y2-7Y+3
We move all terms to the left:
-(Y2-7Y+3)=0
We add all the numbers together, and all the variables
-(+Y^2-7Y+3)=0
We get rid of parentheses
-Y^2+7Y-3=0
We add all the numbers together, and all the variables
-1Y^2+7Y-3=0
a = -1; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-1)·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{37}}{2*-1}=\frac{-7-\sqrt{37}}{-2} $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{37}}{2*-1}=\frac{-7+\sqrt{37}}{-2} $

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