8x-3x(2x-9)=1

Solution for 8x-3x(2x-9)=1 equation:

8x-3x(2x-9)=1

We move all terms to the left:

8x-3x(2x-9)-(1)=0

We multiply parentheses

-6x^2+8x+27x-1=0

We add all the numbers together, and all the variables

-6x^2+35x-1=0

a = -6; b = 35; c = -1;
Δ = b2-4ac
Δ = 352-4·(-6)·(-1)
Δ = 1201
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{-(35)-\sqrt{1201}}{2*-6}=\frac{-35-\sqrt{1201}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1201}}{2*-6}=\frac{-35+\sqrt{1201}}{-12}
$