x^2-16x=130

Solution for x^2-16x=130 equation:

x^2-16x=130

We move all terms to the left:

x^2-16x-(130)=0

a = 1; b = -16; c = -130;
Δ = b2-4ac
Δ = -162-4·1·(-130)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{194}}{2*1}=\frac{16-2\sqrt{194}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{194}}{2*1}=\frac{16+2\sqrt{194}}{2}
$