1/5*x=15

Solution for 1/5*x=15 equation:

1/5*x=15

We move all terms to the left:

1/5*x-(15)=0


Domain of the equation: 5*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-15*5*x+1=0

Wy multiply elements

-75x*x+1=0

Wy multiply elements

-75x^2+1=0

a = -75; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-75)·1
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-75}=\frac{0-10\sqrt{3}}{-150}
=-\frac{10\sqrt{3}}{-150}
=-\frac{\sqrt{3}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-75}=\frac{0+10\sqrt{3}}{-150}
=\frac{10\sqrt{3}}{-150}
=\frac{\sqrt{3}}{-15}
$