I(x)=(20+x)(300-6x)

Solution for I(x)=(20+x)(300-6x) equation:

(I)=(20+I)(300-6I)

We move all terms to the left:

(I)-((20+I)(300-6I))=0

We add all the numbers together, and all the variables

I-((I+20)(-6I+300))=0

We multiply parentheses ..

-((-6I^2+300I-120I+6000))+I=0


We calculate terms in parentheses: -((-6I^2+300I-120I+6000)), so:

(-6I^2+300I-120I+6000)

We get rid of parentheses

-6I^2+300I-120I+6000

We add all the numbers together, and all the variables

-6I^2+180I+6000

Back to the equation:

-(-6I^2+180I+6000)


We get rid of parentheses

6I^2-180I+I-6000=0

We add all the numbers together, and all the variables

6I^2-179I-6000=0

a = 6; b = -179; c = -6000;
Δ = b2-4ac
Δ = -1792-4·6·(-6000)
Δ = 176041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-\sqrt{176041}}{2*6}=\frac{179-\sqrt{176041}}{12}
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+\sqrt{176041}}{2*6}=\frac{179+\sqrt{176041}}{12}
$