9x^2-1=15x+5

Solution for 9x^2-1=15x+5 equation:

9x^2-1=15x+5

We move all terms to the left:

9x^2-1-(15x+5)=0

We get rid of parentheses

9x^2-15x-5-1=0

We add all the numbers together, and all the variables

9x^2-15x-6=0

a = 9; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·9·(-6)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*9}=\frac{36}{18}
=2
$