971x-2x^2=5000+20x+x^2

Solution for 971x-2x^2=5000+20x+x^2 equation:

971x-2x^2=5000+20x+x^2

We move all terms to the left:

971x-2x^2-(5000+20x+x^2)=0

We get rid of parentheses

-2x^2-x^2-20x+971x-5000=0

We add all the numbers together, and all the variables

-3x^2+951x-5000=0

a = -3; b = 951; c = -5000;
Δ = b2-4ac
Δ = 9512-4·(-3)·(-5000)
Δ = 844401
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{-(951)-\sqrt{844401}}{2*-3}=\frac{-951-\sqrt{844401}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(951)+\sqrt{844401}}{2*-3}=\frac{-951+\sqrt{844401}}{-6}
$