(3x-4)(10x+9)=0

Solution for (3x-4)(10x+9)=0 equation:

(3x-4)(10x+9)=0

We multiply parentheses ..

(+30x^2+27x-40x-36)=0

We get rid of parentheses

30x^2+27x-40x-36=0

We add all the numbers together, and all the variables

30x^2-13x-36=0

a = 30; b = -13; c = -36;
Δ = b2-4ac
Δ = -132-4·30·(-36)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-67}{2*30}=\frac{-54}{60}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+67}{2*30}=\frac{80}{60}
=1+1/3
$