(6x-5)(2x-10)=x

Solution for (6x-5)(2x-10)=x equation:

(6x-5)(2x-10)=x

We move all terms to the left:

(6x-5)(2x-10)-(x)=0

We add all the numbers together, and all the variables

-1x+(6x-5)(2x-10)=0

We multiply parentheses ..

(+12x^2-60x-10x+50)-1x=0

We get rid of parentheses

12x^2-60x-10x-1x+50=0

We add all the numbers together, and all the variables

12x^2-71x+50=0

a = 12; b = -71; c = +50;
Δ = b2-4ac
Δ = -712-4·12·50
Δ = 2641
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{-(-71)-\sqrt{2641}}{2*12}=\frac{71-\sqrt{2641}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{2641}}{2*12}=\frac{71+\sqrt{2641}}{24}
$