61r^2+90r+16=r^2-2r

Solution for 61r^2+90r+16=r^2-2r equation:

61r^2+90r+16=r^2-2r

We move all terms to the left:

61r^2+90r+16-(r^2-2r)=0

We get rid of parentheses

61r^2-r^2+90r+2r+16=0

We add all the numbers together, and all the variables

60r^2+92r+16=0

a = 60; b = 92; c = +16;
Δ = b2-4ac
Δ = 922-4·60·16
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-68}{2*60}=\frac{-160}{120}
=-1+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+68}{2*60}=\frac{-24}{120}
=-1/5
$