(8r+1)(6r-1)=0

Solution for (8r+1)(6r-1)=0 equation:

(8r+1)(6r-1)=0

We multiply parentheses ..

(+48r^2-8r+6r-1)=0

We get rid of parentheses

48r^2-8r+6r-1=0

We add all the numbers together, and all the variables

48r^2-2r-1=0

a = 48; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·48·(-1)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*48}=\frac{-12}{96}
=-1/8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*48}=\frac{16}{96}
=1/6
$