4x+10-1/2x=12

Solution for 4x+10-1/2x=12 equation:

4x+10-1/2x=12

We move all terms to the left:

4x+10-1/2x-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x-1/2x-2=0

We multiply all the terms by the denominator


4x*2x-2*2x-1=0

Wy multiply elements

8x^2-4x-1=0

a = 8; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·8·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*8}=\frac{4-4\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*8}=\frac{4+4\sqrt{3}}{16}
$