8x+1=9x^2

Solution for 8x+1=9x^2 equation:

8x+1=9x^2

We move all terms to the left:

8x+1-(9x^2)=0

determiningTheFunctionDomain
-9x^2+8x+1=0

a = -9; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-9)·1
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-9}=\frac{-18}{-18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-9}=\frac{2}{-18}
=-1/9
$