(300-10x)(3.5+.1x)=x

Solution for (300-10x)(3.5+.1x)=x equation:

(300-10x)(3.5+.1x)=x

We move all terms to the left:

(300-10x)(3.5+.1x)-(x)=0

We add all the numbers together, and all the variables

(-10x+300)(.1x+3.5)-x=0

We add all the numbers together, and all the variables

-1x+(-10x+300)(.1x+3.5)=0

We multiply parentheses ..

(-10x^2-35x+300x+1050)-1x=0

We get rid of parentheses

-10x^2-35x+300x-1x+1050=0

We add all the numbers together, and all the variables

-10x^2+264x+1050=0

a = -10; b = 264; c = +1050;
Δ = b2-4ac
Δ = 2642-4·(-10)·1050
Δ = 111696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{111696}=\sqrt{16*6981}=\sqrt{16}*\sqrt{6981}=4\sqrt{6981}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-4\sqrt{6981}}{2*-10}=\frac{-264-4\sqrt{6981}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+4\sqrt{6981}}{2*-10}=\frac{-264+4\sqrt{6981}}{-20}
$