3x-3(x+3)(4x-3)=17x-5

Solution for 3x-3(x+3)(4x-3)=17x-5 equation:

3x-3(x+3)(4x-3)=17x-5

We move all terms to the left:

3x-3(x+3)(4x-3)-(17x-5)=0

We get rid of parentheses

3x-3(x+3)(4x-3)-17x+5=0

We multiply parentheses ..

-3(+4x^2-3x+12x-9)+3x-17x+5=0

We add all the numbers together, and all the variables

-3(+4x^2-3x+12x-9)-14x+5=0

We multiply parentheses

-12x^2+9x-36x-14x+27+5=0

We add all the numbers together, and all the variables

-12x^2-41x+32=0

a = -12; b = -41; c = +32;
Δ = b2-4ac
Δ = -412-4·(-12)·32
Δ = 3217
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{-(-41)-\sqrt{3217}}{2*-12}=\frac{41-\sqrt{3217}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{3217}}{2*-12}=\frac{41+\sqrt{3217}}{-24}
$