r^2+14r-50=9

Solution for r^2+14r-50=9 equation:

r^2+14r-50=9

We move all terms to the left:

r^2+14r-50-(9)=0

We add all the numbers together, and all the variables

r^2+14r-59=0

a = 1; b = 14; c = -59;
Δ = b2-4ac
Δ = 142-4·1·(-59)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12\sqrt{3}}{2*1}=\frac{-14-12\sqrt{3}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12\sqrt{3}}{2*1}=\frac{-14+12\sqrt{3}}{2}
$