5y+(y^2)=4.5

Solution for 5y+(y^2)=4.5 equation:

5y+(y^2)=4.5

We move all terms to the left:

5y+(y^2)-(4.5)=0

determiningTheFunctionDomain
y^2+5y-(4.5)=0

We add all the numbers together, and all the variables

y^2+5y-4.5=0

a = 1; b = 5; c = -4.5;
Δ = b2-4ac
Δ = 52-4·1·(-4.5)
Δ = 43
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{43}}{2*1}=\frac{-5-\sqrt{43}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{43}}{2*1}=\frac{-5+\sqrt{43}}{2}
$