r^2+10r-52=0

Solution for r^2+10r-52=0 equation:

r^2+10r-52=0

a = 1; b = 10; c = -52;
Δ = b2-4ac
Δ = 102-4·1·(-52)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{77}}{2*1}=\frac{-10-2\sqrt{77}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{77}}{2*1}=\frac{-10+2\sqrt{77}}{2}
$