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=4Y-1/2Y-5
We move all terms to the left:
-(4Y-1/2Y-5)=0
Domain of the equation: 2Y-5)!=0We get rid of parentheses
Y∈R
-4Y+1/2Y+5=0
We multiply all the terms by the denominator
-4Y*2Y+5*2Y+1=0
Wy multiply elements
-8Y^2+10Y+1=0
a = -8; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-8)·1
Δ = 132
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*-8}=\frac{-10-2\sqrt{33}}{-16} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*-8}=\frac{-10+2\sqrt{33}}{-16} $
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