6r+4=-r2

Solution for 6r+4=-r2 equation:

6r+4=-r2

We move all terms to the left:

6r+4-(-r2)=0

We add all the numbers together, and all the variables

-(-1r^2)+6r+4=0

We get rid of parentheses

1r^2+6r+4=0

We add all the numbers together, and all the variables

r^2+6r+4=0

a = 1; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·1·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*1}=\frac{-6-2\sqrt{5}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*1}=\frac{-6+2\sqrt{5}}{2}
$