X^2-16x+61=7

Solution for X^2-16x+61=7 equation:

X^2-16X+61=7

We move all terms to the left:

X^2-16X+61-(7)=0

We add all the numbers together, and all the variables

X^2-16X+54=0

a = 1; b = -16; c = +54;
Δ = b2-4ac
Δ = -162-4·1·54
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{10}}{2*1}=\frac{16-2\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{10}}{2*1}=\frac{16+2\sqrt{10}}{2}
$