9x^2-16x-7=2x-9

Solution for 9x^2-16x-7=2x-9 equation:

9x^2-16x-7=2x-9

We move all terms to the left:

9x^2-16x-7-(2x-9)=0

We get rid of parentheses

9x^2-16x-2x+9-7=0

We add all the numbers together, and all the variables

9x^2-18x+2=0

a = 9; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·9·2
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{7}}{2*9}=\frac{18-6\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{7}}{2*9}=\frac{18+6\sqrt{7}}{18}
$