x-3/5x=40

Solution for x-3/5x=40 equation:

x-3/5x=40

We move all terms to the left:

x-3/5x-(40)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-40*5x-3=0

Wy multiply elements

5x^2-200x-3=0

a = 5; b = -200; c = -3;
Δ = b2-4ac
Δ = -2002-4·5·(-3)
Δ = 40060
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:

$\sqrt{\Delta}=\sqrt{40060}=\sqrt{4*10015}=\sqrt{4}*\sqrt{10015}=2\sqrt{10015}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{10015}}{2*5}=\frac{200-2\sqrt{10015}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{10015}}{2*5}=\frac{200+2\sqrt{10015}}{10}
$