20-7/x=2x

Solution for 20-7/x=2x equation:

20-7/x=2x

We move all terms to the left:

20-7/x-(2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x-7/x+20=0

We multiply all the terms by the denominator


-2x*x+20*x-7=0

We add all the numbers together, and all the variables

20x-2x*x-7=0

Wy multiply elements

-2x^2+20x-7=0

a = -2; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·(-2)·(-7)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{86}}{2*-2}=\frac{-20-2\sqrt{86}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{86}}{2*-2}=\frac{-20+2\sqrt{86}}{-4}
$