45=9(u-1)u=-8

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Solution for 45=9(u-1)u=-8 equation:



45=9(u-1)u=-8
We move all terms to the left:
45-(9(u-1)u)=0
We calculate terms in parentheses: -(9(u-1)u), so:
9(u-1)u
We multiply parentheses
9u^2-9u
Back to the equation:
-(9u^2-9u)
We get rid of parentheses
-9u^2+9u+45=0
a = -9; b = 9; c = +45;
Δ = b2-4ac
Δ = 92-4·(-9)·45
Δ = 1701
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{21}}{2*-9}=\frac{-9-9\sqrt{21}}{-18} $
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{21}}{2*-9}=\frac{-9+9\sqrt{21}}{-18} $

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