x(x+5)=(x+1)2+26

Solution for x(x+5)=(x+1)2+26 equation:

x(x+5)=(x+1)2+26

We move all terms to the left:

x(x+5)-((x+1)2+26)=0

We multiply parentheses

x^2+5x-((x+1)2+26)=0


We calculate terms in parentheses: -((x+1)2+26), so:

(x+1)2+26

We multiply parentheses

2x+2+26

We add all the numbers together, and all the variables

2x+28

Back to the equation:

-(2x+28)


We get rid of parentheses

x^2+5x-2x-28=0

We add all the numbers together, and all the variables

x^2+3x-28=0

a = 1; b = 3; c = -28;
Δ = b2-4ac
Δ = 32-4·1·(-28)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-11}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*1}=\frac{8}{2}
=4
$