x-3/5x=30

Solution for x-3/5x=30 equation:

x-3/5x=30

We move all terms to the left:

x-3/5x-(30)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-30*5x-3=0

Wy multiply elements

5x^2-150x-3=0

a = 5; b = -150; c = -3;
Δ = b2-4ac
Δ = -1502-4·5·(-3)
Δ = 22560
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:

$\sqrt{\Delta}=\sqrt{22560}=\sqrt{16*1410}=\sqrt{16}*\sqrt{1410}=4\sqrt{1410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-4\sqrt{1410}}{2*5}=\frac{150-4\sqrt{1410}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+4\sqrt{1410}}{2*5}=\frac{150+4\sqrt{1410}}{10}
$