0=(2x-1)(5x-2)

Solution for 0=(2x-1)(5x-2) equation:

0=(2x-1)(5x-2)

We move all terms to the left:

0-((2x-1)(5x-2))=0

We add all the numbers together, and all the variables

-((2x-1)(5x-2))=0

We multiply parentheses ..

-((+10x^2-4x-5x+2))=0


We calculate terms in parentheses: -((+10x^2-4x-5x+2)), so:

(+10x^2-4x-5x+2)

We get rid of parentheses

10x^2-4x-5x+2

We add all the numbers together, and all the variables

10x^2-9x+2

Back to the equation:

-(10x^2-9x+2)


We get rid of parentheses

-10x^2+9x-2=0

a = -10; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-10)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-10}=\frac{-10}{-20}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-10}=\frac{-8}{-20}
=2/5
$