(80+x)(300-3x)-10(300-3x)=0

Solution for (80+x)(300-3x)-10(300-3x)=0 equation:

(80+x)(300-3x)-10(300-3x)=0

We add all the numbers together, and all the variables

(x+80)(-3x+300)-10(-3x+300)=0

We multiply parentheses

(x+80)(-3x+300)+30x-3000=0

We multiply parentheses ..

(-3x^2+300x-240x+24000)+30x-3000=0

We get rid of parentheses

-3x^2+300x-240x+30x+24000-3000=0

We add all the numbers together, and all the variables

-3x^2+90x+21000=0

a = -3; b = 90; c = +21000;
Δ = b2-4ac
Δ = 902-4·(-3)·21000
Δ = 260100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{260100}=510$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-510}{2*-3}=\frac{-600}{-6}
=+100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+510}{2*-3}=\frac{420}{-6}
=-70
$