3062.20+1.76x=8x-(.002x^2)

Solution for 3062.20+1.76x=8x-(.002x^2) equation:

3062.20+1.76x=8x-(.002x^2)

We move all terms to the left:

3062.20+1.76x-(8x-(.002x^2))=0

We add all the numbers together, and all the variables

1.76x-(8x-(.002x^2))+3062.2=0


We calculate terms in parentheses: -(8x-(.002x^2)), so:

8x-(.002x^2)

We get rid of parentheses

-.002x^2+8x

We add all the numbers together, and all the variables

-0.002x^2+8x

Back to the equation:

-(-0.002x^2+8x)


We get rid of parentheses

0.002x^2-8x+1.76x+3062.2=0

We add all the numbers together, and all the variables

0.002x^2-6.24x+3062.2=0

a = 0.002; b = -6.24; c = +3062.2;
Δ = b2-4ac
Δ = -6.242-4·0.002·3062.2
Δ = 14.44
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{-(-6.24)-\sqrt{14.44}}{2*0.002}=\frac{6.24-\sqrt{14.44}}{0.004}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.24)+\sqrt{14.44}}{2*0.002}=\frac{6.24+\sqrt{14.44}}{0.004}
$