40+1/2x=3x

Solution for 40+1/2x=3x equation:

40+1/2x=3x

We move all terms to the left:

40+1/2x-(3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/2x+40=0

We multiply all the terms by the denominator


-3x*2x+40*2x+1=0

Wy multiply elements

-6x^2+80x+1=0

a = -6; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·(-6)·1
Δ = 6424
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:

$\sqrt{\Delta}=\sqrt{6424}=\sqrt{4*1606}=\sqrt{4}*\sqrt{1606}=2\sqrt{1606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1606}}{2*-6}=\frac{-80-2\sqrt{1606}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1606}}{2*-6}=\frac{-80+2\sqrt{1606}}{-12}
$