1/5x=3x-112

Solution for 1/5x=3x-112 equation:

1/5x=3x-112

We move all terms to the left:

1/5x-(3x-112)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-3x+112=0

We multiply all the terms by the denominator


-3x*5x+112*5x+1=0

Wy multiply elements

-15x^2+560x+1=0

a = -15; b = 560; c = +1;
Δ = b2-4ac
Δ = 5602-4·(-15)·1
Δ = 313660
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:

$\sqrt{\Delta}=\sqrt{313660}=\sqrt{4*78415}=\sqrt{4}*\sqrt{78415}=2\sqrt{78415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(560)-2\sqrt{78415}}{2*-15}=\frac{-560-2\sqrt{78415}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(560)+2\sqrt{78415}}{2*-15}=\frac{-560+2\sqrt{78415}}{-30}
$