240/(x+2)*2+4x=240

Solution for 240/(x+2)*2+4x=240 equation:

240/(x+2)*2+4x=240

We move all terms to the left:

240/(x+2)*2+4x-(240)=0


Domain of the equation: (x+2)*2!=0

x∈R


We add all the numbers together, and all the variables

4x+240/(x+2)*2-240=0

We multiply all the terms by the denominator


4x*(x+2)*2-240*(x+2)*2+240=0

We multiply parentheses

8x^2+16x-480x-960+240=0

We add all the numbers together, and all the variables

8x^2-464x-720=0

a = 8; b = -464; c = -720;
Δ = b2-4ac
Δ = -4642-4·8·(-720)
Δ = 238336
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:

$\sqrt{\Delta}=\sqrt{238336}=\sqrt{12544*19}=\sqrt{12544}*\sqrt{19}=112\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-464)-112\sqrt{19}}{2*8}=\frac{464-112\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-464)+112\sqrt{19}}{2*8}=\frac{464+112\sqrt{19}}{16}
$