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-16=0

a = 9; b = -18; c = -16;
Δ = b2-4ac
Δ = -182-4·9·(-16)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*9}=\frac{48}{18}
=2+2/3
$