2y+(y*y)=19

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Solution for 2y+(y*y)=19 equation:



2y+(y*y)=19
We move all terms to the left:
2y+(y*y)-(19)=0
We add all the numbers together, and all the variables
2y+(+y*y)-19=0
We get rid of parentheses
2y+y*y-19=0
Wy multiply elements
y^2+2y-19=0
a = 1; b = 2; c = -19;
Δ = b2-4ac
Δ = 22-4·1·(-19)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{5}}{2*1}=\frac{-2-4\sqrt{5}}{2} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{5}}{2*1}=\frac{-2+4\sqrt{5}}{2} $

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