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

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

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

We multiply parentheses ..

(+12x^2+15x-16x-20)=0

We get rid of parentheses

12x^2+15x-16x-20=0

We add all the numbers together, and all the variables

12x^2-1x-20=0

a = 12; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·12·(-20)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*12}=\frac{-30}{24}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*12}=\frac{32}{24}
=1+1/3
$