Y=2x(x-3)=-5

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Solution for Y=2x(x-3)=-5 equation:



=2Y(Y-3)=-5
We move all terms to the left:
-(2Y(Y-3))=0
We calculate terms in parentheses: -(2Y(Y-3)), so:
2Y(Y-3)
We multiply parentheses
2Y^2-6Y
Back to the equation:
-(2Y^2-6Y)
We get rid of parentheses
-2Y^2+6Y=0
a = -2; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-2}=\frac{-12}{-4} =+3 $
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-2}=\frac{0}{-4} =0 $

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