(8x+6)(2x-6)=x

Solution for (8x+6)(2x-6)=x equation:

(8x+6)(2x-6)=x

We move all terms to the left:

(8x+6)(2x-6)-(x)=0

We add all the numbers together, and all the variables

-1x+(8x+6)(2x-6)=0

We multiply parentheses ..

(+16x^2-48x+12x-36)-1x=0

We get rid of parentheses

16x^2-48x+12x-1x-36=0

We add all the numbers together, and all the variables

16x^2-37x-36=0

a = 16; b = -37; c = -36;
Δ = b2-4ac
Δ = -372-4·16·(-36)
Δ = 3673
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{-(-37)-\sqrt{3673}}{2*16}=\frac{37-\sqrt{3673}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{3673}}{2*16}=\frac{37+\sqrt{3673}}{32}
$