32+6=5r2

Solution for 32+6=5r2 equation:

32+6=5r^2

We move all terms to the left:

32+6-(5r^2)=0

We add all the numbers together, and all the variables

-5r^2+38=0

a = -5; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-5)·38
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*-5}=\frac{0-2\sqrt{190}}{-10}
=-\frac{2\sqrt{190}}{-10}
=-\frac{\sqrt{190}}{-5}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*-5}=\frac{0+2\sqrt{190}}{-10}
=\frac{2\sqrt{190}}{-10}
=\frac{\sqrt{190}}{-5}
$