5/2x=2x+10

Solution for 5/2x=2x+10 equation:

5/2x=2x+10

We move all terms to the left:

5/2x-(2x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-2x-10=0

We multiply all the terms by the denominator


-2x*2x-10*2x+5=0

Wy multiply elements

-4x^2-20x+5=0

a = -4; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·(-4)·5
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*-4}=\frac{20-4\sqrt{30}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*-4}=\frac{20+4\sqrt{30}}{-8}
$