3x+4=5/4x+3

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

3x+4=5/4x+3

We move all terms to the left:

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


Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

3x-5/4x-3+4=0

We multiply all the terms by the denominator


3x*4x-3*4x+4*4x-5=0

Wy multiply elements

12x^2-12x+16x-5=0

We add all the numbers together, and all the variables

12x^2+4x-5=0

a = 12; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·12·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*12}=\frac{-20}{24}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*12}=\frac{12}{24}
=1/2
$