5r^2+22r+13=5

Solution for 5r^2+22r+13=5 equation:

5r^2+22r+13=5

We move all terms to the left:

5r^2+22r+13-(5)=0

We add all the numbers together, and all the variables

5r^2+22r+8=0

a = 5; b = 22; c = +8;
Δ = b2-4ac
Δ = 222-4·5·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*5}=\frac{-40}{10}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*5}=\frac{-4}{10}
=-2/5
$