Y=x2+13x+42

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Solution for Y=x2+13x+42 equation:



=Y2+13Y+42
We move all terms to the left:
-(Y2+13Y+42)=0
We add all the numbers together, and all the variables
-(+Y^2+13Y+42)=0
We get rid of parentheses
-Y^2-13Y-42=0
We add all the numbers together, and all the variables
-1Y^2-13Y-42=0
a = -1; b = -13; c = -42;
Δ = b2-4ac
Δ = -132-4·(-1)·(-42)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*-1}=\frac{12}{-2} =-6 $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*-1}=\frac{14}{-2} =-7 $

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