45=9(u-1)u=2

Solution for 45=9(u-1)u=2 equation:

45=9(u-1)u=2

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}
$