6^2=x*(5+x)

Solution for 6^2=x*(5+x) equation:

6^2=x(5+x)

We move all terms to the left:

6^2-(x(5+x))=0

We add all the numbers together, and all the variables

-(x(x+5))+6^2=0

We add all the numbers together, and all the variables

-(x(x+5))+36=0


We calculate terms in parentheses: -(x(x+5)), so:

x(x+5)

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x+36=0

We add all the numbers together, and all the variables

-1x^2-5x+36=0

a = -1; b = -5; c = +36;
Δ = b2-4ac
Δ = -52-4·(-1)·36
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-1}=\frac{18}{-2}
=-9
$