1/5x-4=3x+16

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

1/5x-4=3x+16

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2-80x-20x+1=0

We add all the numbers together, and all the variables

-15x^2-100x+1=0

a = -15; b = -100; c = +1;
Δ = b2-4ac
Δ = -1002-4·(-15)·1
Δ = 10060
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:

$\sqrt{\Delta}=\sqrt{10060}=\sqrt{4*2515}=\sqrt{4}*\sqrt{2515}=2\sqrt{2515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2515}}{2*-15}=\frac{100-2\sqrt{2515}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2515}}{2*-15}=\frac{100+2\sqrt{2515}}{-30}
$