9x(2x+1)=5

Solution for 9x(2x+1)=5 equation:

9x(2x+1)=5

We move all terms to the left:

9x(2x+1)-(5)=0

We multiply parentheses

18x^2+9x-5=0

a = 18; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·18·(-5)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*18}=\frac{-30}{36}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*18}=\frac{12}{36}
=1/3
$