(3x-4)(2x+6)=0

Solution for (3x-4)(2x+6)=0 equation:

(3x-4)(2x+6)=0

We multiply parentheses ..

(+6x^2+18x-8x-24)=0

We get rid of parentheses

6x^2+18x-8x-24=0

We add all the numbers together, and all the variables

6x^2+10x-24=0

a = 6; b = 10; c = -24;
Δ = b2-4ac
Δ = 102-4·6·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-26}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+26}{2*6}=\frac{16}{12}
=1+1/3
$