8x-x-3/2x=4

Solution for 8x-x-3/2x=4 equation:

8x-x-3/2x=4

We move all terms to the left:

8x-x-3/2x-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7x-3/2x-4=0

We multiply all the terms by the denominator


7x*2x-4*2x-3=0

Wy multiply elements

14x^2-8x-3=0

a = 14; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·14·(-3)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{58}}{2*14}=\frac{8-2\sqrt{58}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{58}}{2*14}=\frac{8+2\sqrt{58}}{28}
$