(4x-9)(2x+6)=x

Solution for (4x-9)(2x+6)=x equation:

(4x-9)(2x+6)=x

We move all terms to the left:

(4x-9)(2x+6)-(x)=0

We add all the numbers together, and all the variables

-1x+(4x-9)(2x+6)=0

We multiply parentheses ..

(+8x^2+24x-18x-54)-1x=0

We get rid of parentheses

8x^2+24x-18x-1x-54=0

We add all the numbers together, and all the variables

8x^2+5x-54=0

a = 8; b = 5; c = -54;
Δ = b2-4ac
Δ = 52-4·8·(-54)
Δ = 1753
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{-(5)-\sqrt{1753}}{2*8}=\frac{-5-\sqrt{1753}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1753}}{2*8}=\frac{-5+\sqrt{1753}}{16}
$