(45-2x)(x)-2=0

Solution for (45-2x)(x)-2=0 equation:

(45-2x)(x)-2=0

We add all the numbers together, and all the variables

(-2x+45)x-2=0

We multiply parentheses

-2x^2+45x-2=0

a = -2; b = 45; c = -2;
Δ = b2-4ac
Δ = 452-4·(-2)·(-2)
Δ = 2009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-7\sqrt{41}}{2*-2}=\frac{-45-7\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+7\sqrt{41}}{2*-2}=\frac{-45+7\sqrt{41}}{-4}
$