(9x-13)(5x+23)=0

Solution for (9x-13)(5x+23)=0 equation:

(9x-13)(5x+23)=0

We multiply parentheses ..

(+45x^2+207x-65x-299)=0

We get rid of parentheses

45x^2+207x-65x-299=0

We add all the numbers together, and all the variables

45x^2+142x-299=0

a = 45; b = 142; c = -299;
Δ = b2-4ac
Δ = 1422-4·45·(-299)
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(142)-272}{2*45}=\frac{-414}{90}
=-4+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(142)+272}{2*45}=\frac{130}{90}
=1+4/9
$