3(x-3)-7(2x-8)(x-1)=0

Solution for 3(x-3)-7(2x-8)(x-1)=0 equation:

3(x-3)-7(2x-8)(x-1)=0

We multiply parentheses

3x-7(2x-8)(x-1)-9=0

We multiply parentheses ..

-7(+2x^2-2x-8x+8)+3x-9=0

We multiply parentheses

-14x^2+14x+56x+3x-56-9=0

We add all the numbers together, and all the variables

-14x^2+73x-65=0

a = -14; b = 73; c = -65;
Δ = b2-4ac
Δ = 732-4·(-14)·(-65)
Δ = 1689
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{-(73)-\sqrt{1689}}{2*-14}=\frac{-73-\sqrt{1689}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73)+\sqrt{1689}}{2*-14}=\frac{-73+\sqrt{1689}}{-28}
$