5/4x+3=5/6x+4

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

5/4x+3=5/6x+4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


30x/24x^2+(-20x)/24x^2-4+3=0

We add all the numbers together, and all the variables

30x/24x^2+(-20x)/24x^2-1=0

We multiply all the terms by the denominator


30x+(-20x)-1*24x^2=0

Wy multiply elements

-24x^2+30x+(-20x)=0

We get rid of parentheses

-24x^2+30x-20x=0

We add all the numbers together, and all the variables

-24x^2+10x=0

a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-24}=\frac{-20}{-48}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48}
=0
$