R(x)=-0.5x^2+14-2

Solution for R(x)=-0.5x^2+14-2 equation:

(R)=-0.5R^2+14-2

We move all terms to the left:

(R)-(-0.5R^2+14-2)=0

We get rid of parentheses

0.5R^2+R-14+2=0

We add all the numbers together, and all the variables

0.5R^2+R-12=0

a = 0.5; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·0.5·(-12)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*0.5}=\frac{-6}{1}
=-6
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*0.5}=\frac{4}{1}
=4
$