5(r+6)=10(r2)

Solution for 5(r+6)=10(r2) equation:

5(r+6)=10(r2)

We move all terms to the left:

5(r+6)-(10(r2))=0

determiningTheFunctionDomain
5(r+6)-10r2=0

We add all the numbers together, and all the variables

-10r^2+5(r+6)=0

We multiply parentheses

-10r^2+5r+30=0

a = -10; b = 5; c = +30;
Δ = b2-4ac
Δ = 52-4·(-10)·30
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*-10}=\frac{-40}{-20}
=+2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*-10}=\frac{30}{-20}
=-1+1/2
$