5/4x+3=3x-4

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

5/4x+3=3x-4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-12x^2+28x+5=0

a = -12; b = 28; c = +5;
Δ = b2-4ac
Δ = 282-4·(-12)·5
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-32}{2*-12}=\frac{-60}{-24}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+32}{2*-12}=\frac{4}{-24}
=-1/6
$