4r^2+18r+13=-2

Solution for 4r^2+18r+13=-2 equation:

4r^2+18r+13=-2

We move all terms to the left:

4r^2+18r+13-(-2)=0

We add all the numbers together, and all the variables

4r^2+18r+15=0

a = 4; b = 18; c = +15;
Δ = b2-4ac
Δ = 182-4·4·15
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{21}}{2*4}=\frac{-18-2\sqrt{21}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{21}}{2*4}=\frac{-18+2\sqrt{21}}{8}
$