8x+3/2x=42x

Solution for 8x+3/2x=42x equation:

8x+3/2x=42x

We move all terms to the left:

8x+3/2x-(42x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-34x+3/2x=0

We multiply all the terms by the denominator


-34x*2x+3=0

Wy multiply elements

-68x^2+3=0

a = -68; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-68)·3
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*-68}=\frac{0-4\sqrt{51}}{-136}
=-\frac{4\sqrt{51}}{-136}
=-\frac{\sqrt{51}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*-68}=\frac{0+4\sqrt{51}}{-136}
=\frac{4\sqrt{51}}{-136}
=\frac{\sqrt{51}}{-34}
$