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=Y2-14Y+1
We move all terms to the left:
-(Y2-14Y+1)=0
We add all the numbers together, and all the variables
-(+Y^2-14Y+1)=0
We get rid of parentheses
-Y^2+14Y-1=0
We add all the numbers together, and all the variables
-1Y^2+14Y-1=0
a = -1; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·(-1)·(-1)
Δ = 192
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{3}}{2*-1}=\frac{-14-8\sqrt{3}}{-2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{3}}{2*-1}=\frac{-14+8\sqrt{3}}{-2} $
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