7r2=-1+8r

Solution for 7r2=-1+8r equation:

7r^2=-1+8r

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

7r^2-8r+1=0

a = 7; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·7·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*7}=\frac{2}{14}
=1/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*7}=\frac{14}{14}
=1
$