(3x+4)(5x-9)=0

Solution for (3x+4)(5x-9)=0 equation:

(3x+4)(5x-9)=0

We multiply parentheses ..

(+15x^2-27x+20x-36)=0

We get rid of parentheses

15x^2-27x+20x-36=0

We add all the numbers together, and all the variables

15x^2-7x-36=0

a = 15; b = -7; c = -36;
Δ = b2-4ac
Δ = -72-4·15·(-36)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-47}{2*15}=\frac{-40}{30}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+47}{2*15}=\frac{54}{30}
=1+4/5
$