(4x-15)(9x+11)=0

Solution for (4x-15)(9x+11)=0 equation:

(4x-15)(9x+11)=0

We multiply parentheses ..

(+36x^2+44x-135x-165)=0

We get rid of parentheses

36x^2+44x-135x-165=0

We add all the numbers together, and all the variables

36x^2-91x-165=0

a = 36; b = -91; c = -165;
Δ = b2-4ac
Δ = -912-4·36·(-165)
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-179}{2*36}=\frac{-88}{72}
=-1+2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+179}{2*36}=\frac{270}{72}
=3+3/4
$