9x(x+4)=1+2x

Solution for 9x(x+4)=1+2x equation:

9x(x+4)=1+2x

We move all terms to the left:

9x(x+4)-(1+2x)=0

We add all the numbers together, and all the variables

9x(x+4)-(2x+1)=0

We multiply parentheses

9x^2+36x-(2x+1)=0

We get rid of parentheses

9x^2+36x-2x-1=0

We add all the numbers together, and all the variables

9x^2+34x-1=0

a = 9; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·9·(-1)
Δ = 1192
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:

$\sqrt{\Delta}=\sqrt{1192}=\sqrt{4*298}=\sqrt{4}*\sqrt{298}=2\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{298}}{2*9}=\frac{-34-2\sqrt{298}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{298}}{2*9}=\frac{-34+2\sqrt{298}}{18}
$