9x^2-4x-1=2x+7

Solution for 9x^2-4x-1=2x+7 equation:

9x^2-4x-1=2x+7

We move all terms to the left:

9x^2-4x-1-(2x+7)=0

We get rid of parentheses

9x^2-4x-2x-7-1=0

We add all the numbers together, and all the variables

9x^2-6x-8=0

a = 9; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·9·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*9}=\frac{24}{18}
=1+1/3
$