X^2-16x=-59

Solution for X^2-16x=-59 equation:

X^2-16X=-59

We move all terms to the left:

X^2-16X-(-59)=0

We add all the numbers together, and all the variables

X^2-16X+59=0

a = 1; b = -16; c = +59;
Δ = b2-4ac
Δ = -162-4·1·59
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{5}}{2*1}=\frac{16-2\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{5}}{2*1}=\frac{16+2\sqrt{5}}{2}
$