5r^2=16-10r

Solution for 5r^2=16-10r equation:

5r^2=16-10r

We move all terms to the left:

5r^2-(16-10r)=0

We add all the numbers together, and all the variables

5r^2-(-10r+16)=0

We get rid of parentheses

5r^2+10r-16=0

a = 5; b = 10; c = -16;
Δ = b2-4ac
Δ = 102-4·5·(-16)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{105}}{2*5}=\frac{-10-2\sqrt{105}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{105}}{2*5}=\frac{-10+2\sqrt{105}}{10}
$