4x(x+2)=50

Solution for 4x(x+2)=50 equation:

4x(x+2)=50

We move all terms to the left:

4x(x+2)-(50)=0

We multiply parentheses

4x^2+8x-50=0

a = 4; b = 8; c = -50;
Δ = b2-4ac
Δ = 82-4·4·(-50)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{6}}{2*4}=\frac{-8-12\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{6}}{2*4}=\frac{-8+12\sqrt{6}}{8}
$