3/3.5x=4x+8

Solution for 3/3.5x=4x+8 equation:

3/3.5x=4x+8

We move all terms to the left:

3/3.5x-(4x+8)=0


Domain of the equation: 3.5x!=0

x!=0/3.5

x!=0

x∈R


We get rid of parentheses

3/3.5x-4x-8=0

We multiply all the terms by the denominator


-4x*3.5x-8*3.5x+3=0

Wy multiply elements

-12x^2-24x+3=0

a = -12; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-12)·3
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*-12}=\frac{24-12\sqrt{5}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*-12}=\frac{24+12\sqrt{5}}{-24}
$