10x-0.001x^2=7000+2x

Solution for 10x-0.001x^2=7000+2x equation:

10x-0.001x^2=7000+2x

We move all terms to the left:

10x-0.001x^2-(7000+2x)=0

We add all the numbers together, and all the variables

-0.001x^2+10x-(2x+7000)=0

We get rid of parentheses

-0.001x^2+10x-2x-7000=0

We add all the numbers together, and all the variables

-0.001x^2+8x-7000=0

a = -0.001; b = 8; c = -7000;
Δ = b2-4ac
Δ = 82-4·(-0.001)·(-7000)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*-0.001}=\frac{-14}{-0.002}
=+7000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*-0.001}=\frac{-2}{-0.002}
=+1000
$