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=3-8Y-Y2
We move all terms to the left:
-(3-8Y-Y2)=0
We add all the numbers together, and all the variables
-(-8Y-1Y^2+3)=0
We get rid of parentheses
1Y^2+8Y-3=0
We add all the numbers together, and all the variables
Y^2+8Y-3=0
a = 1; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·1·(-3)
Δ = 76
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*1}=\frac{-8-2\sqrt{19}}{2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*1}=\frac{-8+2\sqrt{19}}{2} $
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