25x=x^2-16

Solution for 25x=x^2-16 equation:

25x=x^2-16

We move all terms to the left:

25x-(x^2-16)=0

We get rid of parentheses

-x^2+25x+16=0

We add all the numbers together, and all the variables

-1x^2+25x+16=0

a = -1; b = 25; c = +16;
Δ = b2-4ac
Δ = 252-4·(-1)·16
Δ = 689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{689}}{2*-1}=\frac{-25-\sqrt{689}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{689}}{2*-1}=\frac{-25+\sqrt{689}}{-2}
$