4-5/4x=10/6x

Solution for 4-5/4x=10/6x equation:

4-5/4x=10/6x

We move all terms to the left:

4-5/4x-(10/6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5/4x-(+10/6x)+4=0

We get rid of parentheses

-5/4x-10/6x+4=0

We calculate fractions


(-30x)/24x^2+(-40x)/24x^2+4=0

We multiply all the terms by the denominator


(-30x)+(-40x)+4*24x^2=0

Wy multiply elements

96x^2+(-30x)+(-40x)=0

We get rid of parentheses

96x^2-30x-40x=0

We add all the numbers together, and all the variables

96x^2-70x=0

a = 96; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·96·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*96}=\frac{140}{192}
=35/48
$