(2x+3)(8x-9)=0

Solution for (2x+3)(8x-9)=0 equation:

(2x+3)(8x-9)=0

We multiply parentheses ..

(+16x^2-18x+24x-27)=0

We get rid of parentheses

16x^2-18x+24x-27=0

We add all the numbers together, and all the variables

16x^2+6x-27=0

a = 16; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·16·(-27)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*16}=\frac{-48}{32}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*16}=\frac{36}{32}
=1+1/8
$