17r+r2=52

Solution for 17r+r2=52 equation:

17r+r2=52

We move all terms to the left:

17r+r2-(52)=0

We add all the numbers together, and all the variables

r^2+17r-52=0

a = 1; b = 17; c = -52;
Δ = b2-4ac
Δ = 172-4·1·(-52)
Δ = 497
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{-(17)-\sqrt{497}}{2*1}=\frac{-17-\sqrt{497}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{497}}{2*1}=\frac{-17+\sqrt{497}}{2}
$