(3x-5)(4x+6)=0

Solution for (3x-5)(4x+6)=0 equation:

(3x-5)(4x+6)=0

We multiply parentheses ..

(+12x^2+18x-20x-30)=0

We get rid of parentheses

12x^2+18x-20x-30=0

We add all the numbers together, and all the variables

12x^2-2x-30=0

a = 12; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·12·(-30)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*12}=\frac{40}{24}
=1+2/3
$