1=9x2+8x

Solution for 1=9x2+8x equation:

1=9x^2+8x

We move all terms to the left:

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

We get rid of parentheses

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