1/5x-16-3x=4/5x-6

Solution for 1/5x-16-3x=4/5x-6 equation:

1/5x-16-3x=4/5x-6

We move all terms to the left:

1/5x-16-3x-(4/5x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x-6)!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/5x-(4/5x-6)-16=0

We get rid of parentheses

-3x+1/5x-4/5x+6-16=0

We multiply all the terms by the denominator


-3x*5x+6*5x-16*5x+1-4=0

We add all the numbers together, and all the variables

-3x*5x+6*5x-16*5x-3=0

Wy multiply elements

-15x^2+30x-80x-3=0

We add all the numbers together, and all the variables

-15x^2-50x-3=0

a = -15; b = -50; c = -3;
Δ = b2-4ac
Δ = -502-4·(-15)·(-3)
Δ = 2320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-4\sqrt{145}}{2*-15}=\frac{50-4\sqrt{145}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+4\sqrt{145}}{2*-15}=\frac{50+4\sqrt{145}}{-30}
$