R(x)=-(x-26)(x+10)

Solution for R(x)=-(x-26)(x+10) equation:

(R)=-(R-26)(R+10)

We move all terms to the left:

(R)-(-(R-26)(R+10))=0

We multiply parentheses ..

-(-(+R^2+10R-26R-260))+R=0


We calculate terms in parentheses: -(-(+R^2+10R-26R-260)), so:

-(+R^2+10R-26R-260)

We get rid of parentheses

-R^2-10R+26R+260

We add all the numbers together, and all the variables

-1R^2+16R+260

Back to the equation:

-(-1R^2+16R+260)


We get rid of parentheses

1R^2-16R+R-260=0

We add all the numbers together, and all the variables

R^2-15R-260=0

a = 1; b = -15; c = -260;
Δ = b2-4ac
Δ = -152-4·1·(-260)
Δ = 1265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{1265}}{2*1}=\frac{15-\sqrt{1265}}{2}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1265}}{2*1}=\frac{15+\sqrt{1265}}{2}
$