17x(4x-7)=72

Solution for 17x(4x-7)=72 equation:

17x(4x-7)=72

We move all terms to the left:

17x(4x-7)-(72)=0

We multiply parentheses

68x^2-119x-72=0

a = 68; b = -119; c = -72;
Δ = b2-4ac
Δ = -1192-4·68·(-72)
Δ = 33745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-\sqrt{33745}}{2*68}=\frac{119-\sqrt{33745}}{136}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{33745}}{2*68}=\frac{119+\sqrt{33745}}{136}
$