7/30x+8/5x-5/4=11/12

Solution for 7/30x+8/5x-5/4=11/12 equation:

7/30x+8/5x-5/4=11/12

We move all terms to the left:

7/30x+8/5x-5/4-(11/12)=0


Domain of the equation: 30x!=0

x!=0/30

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/30x+8/5x-5/4-(+11/12)=0

We get rid of parentheses

7/30x+8/5x-5/4-11/12=0

We calculate fractions


(-45000x^2)/28800x^2+(-33000x^2)/28800x^2+6720x/28800x^2+46080x/28800x^2=0

We multiply all the terms by the denominator


(-45000x^2)+(-33000x^2)+6720x+46080x=0

We add all the numbers together, and all the variables

(-45000x^2)+(-33000x^2)+52800x=0

We get rid of parentheses

-45000x^2-33000x^2+52800x=0

We add all the numbers together, and all the variables

-78000x^2+52800x=0

a = -78000; b = 52800; c = 0;
Δ = b2-4ac
Δ = 528002-4·(-78000)·0
Δ = 2787840000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2787840000}=52800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52800)-52800}{2*-78000}=\frac{-105600}{-156000}
=44/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52800)+52800}{2*-78000}=\frac{0}{-156000}
=0
$