x(13x-14)=72

Solution for x(13x-14)=72 equation:

x(13x-14)=72

We move all terms to the left:

x(13x-14)-(72)=0

We multiply parentheses

13x^2-14x-72=0

a = 13; b = -14; c = -72;
Δ = b2-4ac
Δ = -142-4·13·(-72)
Δ = 3940
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:

$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{985}}{2*13}=\frac{14-2\sqrt{985}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{985}}{2*13}=\frac{14+2\sqrt{985}}{26}
$