(-3r+12)(8)r=-1/3

Solution for (-3r+12)(8)r=-1/3 equation:

(-3r+12)(8)r=-1/3

We move all terms to the left:

(-3r+12)(8)r-(-1/3)=0

We multiply parentheses

-24r^2+96r-(-1/3)=0

We get rid of parentheses

-24r^2+96r+1/3=0

We multiply all the terms by the denominator


-24r^2*3+96r*3+1=0

Wy multiply elements

-72r^2+288r+1=0

a = -72; b = 288; c = +1;
Δ = b2-4ac
Δ = 2882-4·(-72)·1
Δ = 83232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{83232}=\sqrt{41616*2}=\sqrt{41616}*\sqrt{2}=204\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-204\sqrt{2}}{2*-72}=\frac{-288-204\sqrt{2}}{-144}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+204\sqrt{2}}{2*-72}=\frac{-288+204\sqrt{2}}{-144}
$