16x=x^2-46

Solution for 16x=x^2-46 equation:

16x=x^2-46

We move all terms to the left:

16x-(x^2-46)=0

We get rid of parentheses

-x^2+16x+46=0

We add all the numbers together, and all the variables

-1x^2+16x+46=0

a = -1; b = 16; c = +46;
Δ = b2-4ac
Δ = 162-4·(-1)·46
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{110}}{2*-1}=\frac{-16-2\sqrt{110}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{110}}{2*-1}=\frac{-16+2\sqrt{110}}{-2}
$