8x-5/2x=3

Solution for 8x-5/2x=3 equation:

8x-5/2x=3

We move all terms to the left:

8x-5/2x-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


8x*2x-3*2x-5=0

Wy multiply elements

16x^2-6x-5=0

a = 16; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·16·(-5)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*16}=\frac{6-2\sqrt{89}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*16}=\frac{6+2\sqrt{89}}{32}
$