(4x-1)(x-2)=9

Solution for (4x-1)(x-2)=9 equation:

(4x-1)(x-2)=9

We move all terms to the left:

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

We multiply parentheses ..

(+4x^2-8x-1x+2)-9=0

We get rid of parentheses

4x^2-8x-1x+2-9=0

We add all the numbers together, and all the variables

4x^2-9x-7=0

a = 4; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·4·(-7)
Δ = 193
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{-(-9)-\sqrt{193}}{2*4}=\frac{9-\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{193}}{2*4}=\frac{9+\sqrt{193}}{8}
$