x+4^2=x(x+10)

Solution for x+4^2=x(x+10) equation:

x+4^2=x(x+10)

We move all terms to the left:

x+4^2-(x(x+10))=0

We add all the numbers together, and all the variables

x-(x(x+10))+16=0


We calculate terms in parentheses: -(x(x+10)), so:

x(x+10)

We multiply parentheses

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

-x^2+x-10x+16=0

We add all the numbers together, and all the variables

-1x^2-9x+16=0

a = -1; b = -9; c = +16;
Δ = b2-4ac
Δ = -92-4·(-1)·16
Δ = 145
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{-(-9)-\sqrt{145}}{2*-1}=\frac{9-\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{145}}{2*-1}=\frac{9+\sqrt{145}}{-2}
$