4(2x^2+3x-9)=0

Solution for 4(2x^2+3x-9)=0 equation:

4(2x^2+3x-9)=0

We multiply parentheses

8x^2+12x-36=0

a = 8; b = 12; c = -36;
Δ = b2-4ac
Δ = 122-4·8·(-36)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*8}=\frac{24}{16}
=1+1/2
$