3x-2/4x+3=5

Solution for 3x-2/4x+3=5 equation:

3x-2/4x+3=5

We move all terms to the left:

3x-2/4x+3-(5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/4x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-8x-2=0

a = 12; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·12·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*12}=\frac{8-4\sqrt{10}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*12}=\frac{8+4\sqrt{10}}{24}
$