R(x)=160,000x-1,000x2

Solution for R(x)=160,000x-1,000x2 equation:

(R)=160.000R-1.000R^2

We move all terms to the left:

(R)-(160.000R-1.000R^2)=0

We get rid of parentheses

1.000R^2-160.000R+R=0

We add all the numbers together, and all the variables

R^2-159R=0

a = 1; b = -159; c = 0;
Δ = b2-4ac
Δ = -1592-4·1·0
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-159}{2*1}=\frac{0}{2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+159}{2*1}=\frac{318}{2}
=159
$