4/5*x=30

Solution for 4/5*x=30 equation:

4/5*x=30

We move all terms to the left:

4/5*x-(30)=0


Domain of the equation: 5*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-30*5*x+4=0

Wy multiply elements

-150x*x+4=0

Wy multiply elements

-150x^2+4=0

a = -150; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-150)·4
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*-150}=\frac{0-20\sqrt{6}}{-300}
=-\frac{20\sqrt{6}}{-300}
=-\frac{\sqrt{6}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*-150}=\frac{0+20\sqrt{6}}{-300}
=\frac{20\sqrt{6}}{-300}
=\frac{\sqrt{6}}{-15}
$