X^2+2=16x-61

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

X^2+2=16X-61

We move all terms to the left:

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

We get rid of parentheses

X^2-16X+61+2=0

We add all the numbers together, and all the variables

X^2-16X+63=0

a = 1; b = -16; c = +63;
Δ = b2-4ac
Δ = -162-4·1·63
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2}{2*1}=\frac{14}{2}
=7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2}{2*1}=\frac{18}{2}
=9
$