7r^2+63r=-56

Solution for 7r^2+63r=-56 equation:

7r^2+63r=-56

We move all terms to the left:

7r^2+63r-(-56)=0

We add all the numbers together, and all the variables

7r^2+63r+56=0

a = 7; b = 63; c = +56;
Δ = b2-4ac
Δ = 632-4·7·56
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-49}{2*7}=\frac{-112}{14}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+49}{2*7}=\frac{-14}{14}
=-1
$