x(17x+8)=240

Solution for x(17x+8)=240 equation:

x(17x+8)=240

We move all terms to the left:

x(17x+8)-(240)=0

We multiply parentheses

17x^2+8x-240=0

a = 17; b = 8; c = -240;
Δ = b2-4ac
Δ = 82-4·17·(-240)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-128}{2*17}=\frac{-136}{34}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+128}{2*17}=\frac{120}{34}
=3+9/17
$