(5x+10)/6x-10*5x-x=48

Solution for (5x+10)/6x-10*5x-x=48 equation:

(5x+10)/6x-10*5x-x=48

We move all terms to the left:

(5x+10)/6x-10*5x-x-(48)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+(5x+10)/6x-10*5x-48=0

Wy multiply elements

-1x+(5x+10)/6x-50x-48=0

We multiply all the terms by the denominator


-1x*6x+(5x+10)-50x*6x-48*6x=0

Wy multiply elements

-6x^2-300x^2+(5x+10)-288x=0

We get rid of parentheses

-6x^2-300x^2+5x-288x+10=0

We add all the numbers together, and all the variables

-306x^2-283x+10=0

a = -306; b = -283; c = +10;
Δ = b2-4ac
Δ = -2832-4·(-306)·10
Δ = 92329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-283)-\sqrt{92329}}{2*-306}=\frac{283-\sqrt{92329}}{-612}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-283)+\sqrt{92329}}{2*-306}=\frac{283+\sqrt{92329}}{-612}
$