20/2x+10=x-4

Solution for 20/2x+10=x-4 equation:

20/2x+10=x-4

We move all terms to the left:

20/2x+10-(x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

20/2x-x+4+10=0

We multiply all the terms by the denominator


-x*2x+4*2x+10*2x+20=0

Wy multiply elements

-2x^2+8x+20x+20=0

We add all the numbers together, and all the variables

-2x^2+28x+20=0

a = -2; b = 28; c = +20;
Δ = b2-4ac
Δ = 282-4·(-2)·20
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{59}}{2*-2}=\frac{-28-4\sqrt{59}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{59}}{2*-2}=\frac{-28+4\sqrt{59}}{-4}
$