(3x-17)(x+5)=-64

Solution for (3x-17)(x+5)=-64 equation:

(3x-17)(x+5)=-64

We move all terms to the left:

(3x-17)(x+5)-(-64)=0

We add all the numbers together, and all the variables

(3x-17)(x+5)+64=0

We multiply parentheses ..

(+3x^2+15x-17x-85)+64=0

We get rid of parentheses

3x^2+15x-17x-85+64=0

We add all the numbers together, and all the variables

3x^2-2x-21=0

a = 3; b = -2; c = -21;
Δ = b2-4ac
Δ = -22-4·3·(-21)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*3}=\frac{18}{6}
=3
$