x(x+6)=5(5+3)

Solution for x(x+6)=5(5+3) equation:

x(x+6)=5(5+3)

We move all terms to the left:

x(x+6)-(5(5+3))=0

We add all the numbers together, and all the variables

x(x+6)-(58)=0

We add all the numbers together, and all the variables

x(x+6)-58=0

We multiply parentheses

x^2+6x-58=0

a = 1; b = 6; c = -58;
Δ = b2-4ac
Δ = 62-4·1·(-58)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{67}}{2*1}=\frac{-6-2\sqrt{67}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{67}}{2*1}=\frac{-6+2\sqrt{67}}{2}
$