x(13x+4)=9

Solution for x(13x+4)=9 equation:

x(13x+4)=9

We move all terms to the left:

x(13x+4)-(9)=0

We multiply parentheses

13x^2+4x-9=0

a = 13; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·13·(-9)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-22}{2*13}=\frac{-26}{26}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+22}{2*13}=\frac{18}{26}
=9/13
$