(8)(x)(3x+2)=680

Solution for (8)(x)(3x+2)=680 equation:

(8)(x)(3x+2)=680

We move all terms to the left:

(8)(x)(3x+2)-(680)=0

We multiply parentheses

24x^2+16x-680=0

a = 24; b = 16; c = -680;
Δ = b2-4ac
Δ = 162-4·24·(-680)
Δ = 65536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65536}=256$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-256}{2*24}=\frac{-272}{48}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+256}{2*24}=\frac{240}{48}
=5
$