(3x+2)(6x-5)=x

Solution for (3x+2)(6x-5)=x equation:

(3x+2)(6x-5)=x

We move all terms to the left:

(3x+2)(6x-5)-(x)=0

We add all the numbers together, and all the variables

-1x+(3x+2)(6x-5)=0

We multiply parentheses ..

(+18x^2-15x+12x-10)-1x=0

We get rid of parentheses

18x^2-15x+12x-1x-10=0

We add all the numbers together, and all the variables

18x^2-4x-10=0

a = 18; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·18·(-10)
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*18}=\frac{4-4\sqrt{46}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*18}=\frac{4+4\sqrt{46}}{36}
$