(-3x+8)(-x-2)=63

Solution for (-3x+8)(-x-2)=63 equation:

(-3x+8)(-x-2)=63

We move all terms to the left:

(-3x+8)(-x-2)-(63)=0

We add all the numbers together, and all the variables

(-3x+8)(-1x-2)-63=0

We multiply parentheses ..

(+3x^2+6x-8x-16)-63=0

We get rid of parentheses

3x^2+6x-8x-16-63=0

We add all the numbers together, and all the variables

3x^2-2x-79=0

a = 3; b = -2; c = -79;
Δ = b2-4ac
Δ = -22-4·3·(-79)
Δ = 952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{238}}{2*3}=\frac{2-2\sqrt{238}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{238}}{2*3}=\frac{2+2\sqrt{238}}{6}
$