5/4x=6-3x

Solution for 5/4x=6-3x equation:

5/4x=6-3x

We move all terms to the left:

5/4x-(6-3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(-3x+6)=0

We get rid of parentheses

5/4x+3x-6=0

We multiply all the terms by the denominator


3x*4x-6*4x+5=0

Wy multiply elements

12x^2-24x+5=0

a = 12; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·12·5
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{21}}{2*12}=\frac{24-4\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{21}}{2*12}=\frac{24+4\sqrt{21}}{24}
$