660+3/2x=2x

Solution for 660+3/2x=2x equation:

660+3/2x=2x

We move all terms to the left:

660+3/2x-(2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/2x+660=0

We multiply all the terms by the denominator


-2x*2x+660*2x+3=0

Wy multiply elements

-4x^2+1320x+3=0

a = -4; b = 1320; c = +3;
Δ = b2-4ac
Δ = 13202-4·(-4)·3
Δ = 1742448
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:

$\sqrt{\Delta}=\sqrt{1742448}=\sqrt{16*108903}=\sqrt{16}*\sqrt{108903}=4\sqrt{108903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1320)-4\sqrt{108903}}{2*-4}=\frac{-1320-4\sqrt{108903}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1320)+4\sqrt{108903}}{2*-4}=\frac{-1320+4\sqrt{108903}}{-8}
$