5r2+4=164

Solution for 5r2+4=164 equation:

5r^2+4=164

We move all terms to the left:

5r^2+4-(164)=0

We add all the numbers together, and all the variables

5r^2-160=0

a = 5; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·5·(-160)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*5}=\frac{0-40\sqrt{2}}{10}
=-\frac{40\sqrt{2}}{10}
=-4\sqrt{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*5}=\frac{0+40\sqrt{2}}{10}
=\frac{40\sqrt{2}}{10}
=4\sqrt{2}
$