5x(4+x)=50

Solution for 5x(4+x)=50 equation:

5x(4+x)=50

We move all terms to the left:

5x(4+x)-(50)=0

We add all the numbers together, and all the variables

5x(x+4)-50=0

We multiply parentheses

5x^2+20x-50=0

a = 5; b = 20; c = -50;
Δ = b2-4ac
Δ = 202-4·5·(-50)
Δ = 1400
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:

$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{14}}{2*5}=\frac{-20-10\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{14}}{2*5}=\frac{-20+10\sqrt{14}}{10}
$