(90-10x)(80+5x)=0

Solution for (90-10x)(80+5x)=0 equation:

(90-10x)(80+5x)=0

We add all the numbers together, and all the variables

(-10x+90)(5x+80)=0

We multiply parentheses ..

(-50x^2-800x+450x+7200)=0

We get rid of parentheses

-50x^2-800x+450x+7200=0

We add all the numbers together, and all the variables

-50x^2-350x+7200=0

a = -50; b = -350; c = +7200;
Δ = b2-4ac
Δ = -3502-4·(-50)·7200
Δ = 1562500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1562500}=1250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-1250}{2*-50}=\frac{-900}{-100}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+1250}{2*-50}=\frac{1600}{-100}
=-16
$