16x-61=x2

Solution for 16x-61=x2 equation:

16x-61=x2

We move all terms to the left:

16x-61-(x2)=0

We add all the numbers together, and all the variables

-1x^2+16x-61=0

a = -1; b = 16; c = -61;
Δ = b2-4ac
Δ = 162-4·(-1)·(-61)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{3}}{2*-1}=\frac{-16-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{3}}{2*-1}=\frac{-16+2\sqrt{3}}{-2}
$