(8r+1)(7r-2)=0

Solution for (8r+1)(7r-2)=0 equation:

(8r+1)(7r-2)=0

We multiply parentheses ..

(+56r^2-16r+7r-2)=0

We get rid of parentheses

56r^2-16r+7r-2=0

We add all the numbers together, and all the variables

56r^2-9r-2=0

a = 56; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·56·(-2)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-23}{2*56}=\frac{-14}{112}
=-1/8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+23}{2*56}=\frac{32}{112}
=2/7
$