16590=(240-5x)(73+x)

Solution for 16590=(240-5x)(73+x) equation:

16590=(240-5x)(73+x)

We move all terms to the left:

16590-((240-5x)(73+x))=0

We add all the numbers together, and all the variables

-((-5x+240)(x+73))+16590=0

We multiply parentheses ..

-((-5x^2-365x+240x+17520))+16590=0


We calculate terms in parentheses: -((-5x^2-365x+240x+17520)), so:

(-5x^2-365x+240x+17520)

We get rid of parentheses

-5x^2-365x+240x+17520

We add all the numbers together, and all the variables

-5x^2-125x+17520

Back to the equation:

-(-5x^2-125x+17520)


We get rid of parentheses

5x^2+125x-17520+16590=0

We add all the numbers together, and all the variables

5x^2+125x-930=0

a = 5; b = 125; c = -930;
Δ = b2-4ac
Δ = 1252-4·5·(-930)
Δ = 34225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34225}=185$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-185}{2*5}=\frac{-310}{10}
=-31
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+185}{2*5}=\frac{60}{10}
=6
$