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

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

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

We multiply parentheses

16x^2+24x-72=0

a = 16; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·16·(-72)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-72}{2*16}=\frac{-96}{32}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+72}{2*16}=\frac{48}{32}
=1+1/2
$