x=(20-x)*(300+68*x)

Solution for x=(20-x)*(300+68*x) equation:

x=(20-x)(300+68x)

We move all terms to the left:

x-((20-x)(300+68x))=0

We add all the numbers together, and all the variables

x-((-1x+20)(68x+300))=0

We multiply parentheses ..

-((-68x^2-300x+1360x+6000))+x=0


We calculate terms in parentheses: -((-68x^2-300x+1360x+6000)), so:

(-68x^2-300x+1360x+6000)

We get rid of parentheses

-68x^2-300x+1360x+6000

We add all the numbers together, and all the variables

-68x^2+1060x+6000

Back to the equation:

-(-68x^2+1060x+6000)


We get rid of parentheses

68x^2-1060x+x-6000=0

We add all the numbers together, and all the variables

68x^2-1059x-6000=0

a = 68; b = -1059; c = -6000;
Δ = b2-4ac
Δ = -10592-4·68·(-6000)
Δ = 2753481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1059)-\sqrt{2753481}}{2*68}=\frac{1059-\sqrt{2753481}}{136}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1059)+\sqrt{2753481}}{2*68}=\frac{1059+\sqrt{2753481}}{136}
$