7/4x-7/4+2/3x=5/12

Solution for 7/4x-7/4+2/3x=5/12 equation:

7/4x-7/4+2/3x=5/12

We move all terms to the left:

7/4x-7/4+2/3x-(5/12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7/4x+2/3x-7/4-(+5/12)=0

We get rid of parentheses

7/4x+2/3x-7/4-5/12=0

We calculate fractions


(-720x^2)/2304x^2+252x/2304x^2+1536x/2304x^2+(-252x)/2304x^2=0

We multiply all the terms by the denominator


(-720x^2)+252x+1536x+(-252x)=0

We add all the numbers together, and all the variables

(-720x^2)+1788x+(-252x)=0

We get rid of parentheses

-720x^2+1788x-252x=0

We add all the numbers together, and all the variables

-720x^2+1536x=0

a = -720; b = 1536; c = 0;
Δ = b2-4ac
Δ = 15362-4·(-720)·0
Δ = 2359296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2359296}=1536$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1536)-1536}{2*-720}=\frac{-3072}{-1440}
=2+2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1536)+1536}{2*-720}=\frac{0}{-1440}
=0
$