7r^2=32r-16

Solution for 7r^2=32r-16 equation:

7r^2=32r-16

We move all terms to the left:

7r^2-(32r-16)=0

We get rid of parentheses

7r^2-32r+16=0

a = 7; b = -32; c = +16;
Δ = b2-4ac
Δ = -322-4·7·16
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-24}{2*7}=\frac{8}{14}
=4/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+24}{2*7}=\frac{56}{14}
=4
$