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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-12x+5

Back to the equation:

-(4x^2-12x+5)


We add all the numbers together, and all the variables

x-(4x^2-12x+5)=0

We get rid of parentheses

-4x^2+x+12x-5=0

We add all the numbers together, and all the variables

-4x^2+13x-5=0

a = -4; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-4)·(-5)
Δ = 89
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{-(13)-\sqrt{89}}{2*-4}=\frac{-13-\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{89}}{2*-4}=\frac{-13+\sqrt{89}}{-8}
$