7x(2x+1)=9

Solution for 7x(2x+1)=9 equation:

7x(2x+1)=9

We move all terms to the left:

7x(2x+1)-(9)=0

We multiply parentheses

14x^2+7x-9=0

a = 14; b = 7; c = -9;
Δ = b2-4ac
Δ = 72-4·14·(-9)
Δ = 553
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{-(7)-\sqrt{553}}{2*14}=\frac{-7-\sqrt{553}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{553}}{2*14}=\frac{-7+\sqrt{553}}{28}
$