3x=7/2x+8

Solution for 3x=7/2x+8 equation:

3x=7/2x+8

We move all terms to the left:

3x-(7/2x+8)=0


Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

3x-7/2x-8=0

We multiply all the terms by the denominator


3x*2x-8*2x-7=0

Wy multiply elements

6x^2-16x-7=0

a = 6; b = -16; c = -7;
Δ = b2-4ac
Δ = -162-4·6·(-7)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{106}}{2*6}=\frac{16-2\sqrt{106}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{106}}{2*6}=\frac{16+2\sqrt{106}}{12}
$