(8x-6)(5x+3)-16x^2+9=0

Solution for (8x-6)(5x+3)-16x^2+9=0 equation:

(8x-6)(5x+3)-16x^2+9=0

We multiply parentheses ..

-16x^2+(+40x^2+24x-30x-18)+9=0

We get rid of parentheses

-16x^2+40x^2+24x-30x-18+9=0

We add all the numbers together, and all the variables

24x^2-6x-9=0

a = 24; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·24·(-9)
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{-(-6)-30}{2*24}=\frac{-24}{48}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*24}=\frac{36}{48}
=3/4
$