4r^2+15r+7=-1

Solution for 4r^2+15r+7=-1 equation:

4r^2+15r+7=-1

We move all terms to the left:

4r^2+15r+7-(-1)=0

We add all the numbers together, and all the variables

4r^2+15r+8=0

a = 4; b = 15; c = +8;
Δ = b2-4ac
Δ = 152-4·4·8
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{97}}{2*4}=\frac{-15-\sqrt{97}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{97}}{2*4}=\frac{-15+\sqrt{97}}{8}
$