(6x-3)(2x+13)=x

Solution for (6x-3)(2x+13)=x equation:

(6x-3)(2x+13)=x

We move all terms to the left:

(6x-3)(2x+13)-(x)=0

We add all the numbers together, and all the variables

-1x+(6x-3)(2x+13)=0

We multiply parentheses ..

(+12x^2+78x-6x-39)-1x=0

We get rid of parentheses

12x^2+78x-6x-1x-39=0

We add all the numbers together, and all the variables

12x^2+71x-39=0

a = 12; b = 71; c = -39;
Δ = b2-4ac
Δ = 712-4·12·(-39)
Δ = 6913
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{6913}}{2*12}=\frac{-71-\sqrt{6913}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+\sqrt{6913}}{2*12}=\frac{-71+\sqrt{6913}}{24}
$