7/4x+5=5/6x-4

Solution for 7/4x+5=5/6x-4 equation:

7/4x+5=5/6x-4

We move all terms to the left:

7/4x+5-(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

7/4x-5/6x+4+5=0

We calculate fractions


42x/24x^2+(-20x)/24x^2+4+5=0

We add all the numbers together, and all the variables

42x/24x^2+(-20x)/24x^2+9=0

We multiply all the terms by the denominator


42x+(-20x)+9*24x^2=0

Wy multiply elements

216x^2+42x+(-20x)=0

We get rid of parentheses

216x^2+42x-20x=0

We add all the numbers together, and all the variables

216x^2+22x=0

a = 216; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·216·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*216}=\frac{-44}{432}
=-11/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*216}=\frac{0}{432}
=0
$