8r^2-5r+5=2r+7r^2+5

Solution for 8r^2-5r+5=2r+7r^2+5 equation:

8r^2-5r+5=2r+7r^2+5

We move all terms to the left:

8r^2-5r+5-(2r+7r^2+5)=0

We get rid of parentheses

8r^2-7r^2-2r-5r-5+5=0

We add all the numbers together, and all the variables

r^2-7r=0

a = 1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·1·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*1}=\frac{0}{2}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*1}=\frac{14}{2}
=7
$