1/5x=3x-56

Solution for 1/5x=3x-56 equation:

1/5x=3x-56

We move all terms to the left:

1/5x-(3x-56)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-3x+56=0

We multiply all the terms by the denominator


-3x*5x+56*5x+1=0

Wy multiply elements

-15x^2+280x+1=0

a = -15; b = 280; c = +1;
Δ = b2-4ac
Δ = 2802-4·(-15)·1
Δ = 78460
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:

$\sqrt{\Delta}=\sqrt{78460}=\sqrt{4*19615}=\sqrt{4}*\sqrt{19615}=2\sqrt{19615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-2\sqrt{19615}}{2*-15}=\frac{-280-2\sqrt{19615}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+2\sqrt{19615}}{2*-15}=\frac{-280+2\sqrt{19615}}{-30}
$