r^2-18r-17=7

Solution for r^2-18r-17=7 equation:

r^2-18r-17=7

We move all terms to the left:

r^2-18r-17-(7)=0

We add all the numbers together, and all the variables

r^2-18r-24=0

a = 1; b = -18; c = -24;
Δ = b2-4ac
Δ = -182-4·1·(-24)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*1}=\frac{18-2\sqrt{105}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*1}=\frac{18+2\sqrt{105}}{2}
$