R=-2x^2+130x

Solution for R=-2x^2+130x equation:

=-2R^2+130R

We move all terms to the left:

-(-2R^2+130R)=0

We get rid of parentheses

2R^2-130R=0

a = 2; b = -130; c = 0;
Δ = b2-4ac
Δ = -1302-4·2·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-130}{2*2}=\frac{0}{4}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+130}{2*2}=\frac{260}{4}
=65
$