(5x-3)(6x-6)=x

Solution for (5x-3)(6x-6)=x equation:

(5x-3)(6x-6)=x

We move all terms to the left:

(5x-3)(6x-6)-(x)=0

We add all the numbers together, and all the variables

-1x+(5x-3)(6x-6)=0

We multiply parentheses ..

(+30x^2-30x-18x+18)-1x=0

We get rid of parentheses

30x^2-30x-18x-1x+18=0

We add all the numbers together, and all the variables

30x^2-49x+18=0

a = 30; b = -49; c = +18;
Δ = b2-4ac
Δ = -492-4·30·18
Δ = 241
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{-(-49)-\sqrt{241}}{2*30}=\frac{49-\sqrt{241}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{241}}{2*30}=\frac{49+\sqrt{241}}{60}
$