X^2+16x-61=0

Solution for X^2+16x-61=0 equation:

X^2+16X-61=0

a = 1; b = 16; c = -61;
Δ = b2-4ac
Δ = 162-4·1·(-61)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-10\sqrt{5}}{2*1}=\frac{-16-10\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+10\sqrt{5}}{2*1}=\frac{-16+10\sqrt{5}}{2}
$