(2x-1)(x-2)=0410

Solution for (2x-1)(x-2)=0410 equation:

(2x-1)(x-2)=0410

We move all terms to the left:

(2x-1)(x-2)-(0410)=0

We add all the numbers together, and all the variables

(2x-1)(x-2)-410=0

We multiply parentheses ..

(+2x^2-4x-1x+2)-410=0

We get rid of parentheses

2x^2-4x-1x+2-410=0

We add all the numbers together, and all the variables

2x^2-5x-408=0

a = 2; b = -5; c = -408;
Δ = b2-4ac
Δ = -52-4·2·(-408)
Δ = 3289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{3289}}{2*2}=\frac{5-\sqrt{3289}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{3289}}{2*2}=\frac{5+\sqrt{3289}}{4}
$