5(x+13)=x(4+x)

Solution for 5(x+13)=x(4+x) equation:

5(x+13)=x(4+x)

We move all terms to the left:

5(x+13)-(x(4+x))=0

We add all the numbers together, and all the variables

5(x+13)-(x(x+4))=0

We multiply parentheses

5x-(x(x+4))+65=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2+5x-4x+65=0

We add all the numbers together, and all the variables

-1x^2+x+65=0

a = -1; b = 1; c = +65;
Δ = b2-4ac
Δ = 12-4·(-1)·65
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{29}}{2*-1}=\frac{-1-3\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{29}}{2*-1}=\frac{-1+3\sqrt{29}}{-2}
$