6x-9=16x^2-8x-24

Solution for 6x-9=16x^2-8x-24 equation:

6x-9=16x^2-8x-24

We move all terms to the left:

6x-9-(16x^2-8x-24)=0

We get rid of parentheses

-16x^2+6x+8x+24-9=0

We add all the numbers together, and all the variables

-16x^2+14x+15=0

a = -16; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·(-16)·15
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*-16}=\frac{-48}{-32}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*-16}=\frac{20}{-32}
=-5/8
$