x(5+2x)=50

Solution for x(5+2x)=50 equation:

x(5+2x)=50

We move all terms to the left:

x(5+2x)-(50)=0

We add all the numbers together, and all the variables

x(2x+5)-50=0

We multiply parentheses

2x^2+5x-50=0

a = 2; b = 5; c = -50;
Δ = b2-4ac
Δ = 52-4·2·(-50)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{17}}{2*2}=\frac{-5-5\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{17}}{2*2}=\frac{-5+5\sqrt{17}}{4}
$