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=Y2-12Y-5

We move all terms to the left:

-(Y2-12Y-5)=0

We add all the numbers together, and all the variables

-(+Y^2-12Y-5)=0

We get rid of parentheses

-Y^2+12Y+5=0

We add all the numbers together, and all the variables

-1Y^2+12Y+5=0

a = -1; b = 12; c = +5;

Δ = b^{2}-4ac

Δ = 12^{2}-4·(-1)·5

Δ = 164

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{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{41}}{2*-1}=\frac{-12-2\sqrt{41}}{-2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{41}}{2*-1}=\frac{-12+2\sqrt{41}}{-2} $

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