(4x-3)(8x+5)=-9

Solution for (4x-3)(8x+5)=-9 equation:

(4x-3)(8x+5)=-9

We move all terms to the left:

(4x-3)(8x+5)-(-9)=0

We add all the numbers together, and all the variables

(4x-3)(8x+5)+9=0

We multiply parentheses ..

(+32x^2+20x-24x-15)+9=0

We get rid of parentheses

32x^2+20x-24x-15+9=0

We add all the numbers together, and all the variables

32x^2-4x-6=0

a = 32; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·32·(-6)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*32}=\frac{-24}{64}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*32}=\frac{32}{64}
=1/2
$