(9x-20)(5x+16)=0

Solution for (9x-20)(5x+16)=0 equation:

(9x-20)(5x+16)=0

We multiply parentheses ..

(+45x^2+144x-100x-320)=0

We get rid of parentheses

45x^2+144x-100x-320=0

We add all the numbers together, and all the variables

45x^2+44x-320=0

a = 45; b = 44; c = -320;
Δ = b2-4ac
Δ = 442-4·45·(-320)
Δ = 59536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59536}=244$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-244}{2*45}=\frac{-288}{90}
=-3+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+244}{2*45}=\frac{200}{90}
=2+2/9
$