9/4x-5-6=-13/12x

Solution for 9/4x-5-6=-13/12x equation:

9/4x-5-6=-13/12x

We move all terms to the left:

9/4x-5-6-(-13/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/4x-(-13/12x)-11=0

We get rid of parentheses

9/4x+13/12x-11=0

We calculate fractions


108x/48x^2+52x/48x^2-11=0

We multiply all the terms by the denominator


108x+52x-11*48x^2=0

We add all the numbers together, and all the variables

160x-11*48x^2=0

Wy multiply elements

-528x^2+160x=0

a = -528; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·(-528)·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*-528}=\frac{-320}{-1056}
=10/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*-528}=\frac{0}{-1056}
=0
$