(-3x-8)(x-8)=69

Solution for (-3x-8)(x-8)=69 equation:

(-3x-8)(x-8)=69

We move all terms to the left:

(-3x-8)(x-8)-(69)=0

We multiply parentheses ..

(-3x^2+24x-8x+64)-69=0

We get rid of parentheses

-3x^2+24x-8x+64-69=0

We add all the numbers together, and all the variables

-3x^2+16x-5=0

a = -3; b = 16; c = -5;
Δ = b2-4ac
Δ = 162-4·(-3)·(-5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-14}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+14}{2*-3}=\frac{-2}{-6}
=1/3
$