45=2n2-5n+3

Solution for 45=2n2-5n+3 equation:

45=2n^2-5n+3

We move all terms to the left:

45-(2n^2-5n+3)=0

We get rid of parentheses

-2n^2+5n-3+45=0

We add all the numbers together, and all the variables

-2n^2+5n+42=0

a = -2; b = 5; c = +42;
Δ = b2-4ac
Δ = 52-4·(-2)·42
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*-2}=\frac{-24}{-4}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-2}=\frac{14}{-4}
=-3+1/2
$