2u2-9u+13=(u-1)2

Solution for 2u2-9u+13=(u-1)2 equation:

2u^2-9u+13=(u-1)2

We move all terms to the left:

2u^2-9u+13-((u-1)2)=0


We calculate terms in parentheses: -((u-1)2), so:

(u-1)2

We multiply parentheses

2u-2

Back to the equation:

-(2u-2)


We get rid of parentheses

2u^2-9u-2u+2+13=0

We add all the numbers together, and all the variables

2u^2-11u+15=0

a = 2; b = -11; c = +15;
Δ = b2-4ac
Δ = -112-4·2·15
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*2}=\frac{10}{4}
=2+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*2}=\frac{12}{4}
=3
$