r^2+14r-101=9

Solution for r^2+14r-101=9 equation:

r^2+14r-101=9

We move all terms to the left:

r^2+14r-101-(9)=0

We add all the numbers together, and all the variables

r^2+14r-110=0

a = 1; b = 14; c = -110;
Δ = b2-4ac
Δ = 142-4·1·(-110)
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{159}}{2*1}=\frac{-14-2\sqrt{159}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{159}}{2*1}=\frac{-14+2\sqrt{159}}{2}
$