4x+10-1/2x=22

Solution for 4x+10-1/2x=22 equation:

4x+10-1/2x=22

We move all terms to the left:

4x+10-1/2x-(22)=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-12=0

We multiply all the terms by the denominator


4x*2x-12*2x-1=0

Wy multiply elements

8x^2-24x-1=0

a = 8; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·8·(-1)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{38}}{2*8}=\frac{24-4\sqrt{38}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{38}}{2*8}=\frac{24+4\sqrt{38}}{16}
$