x-2/5x=42

Solution for x-2/5x=42 equation:

x-2/5x=42

We move all terms to the left:

x-2/5x-(42)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-42*5x-2=0

Wy multiply elements

5x^2-210x-2=0

a = 5; b = -210; c = -2;
Δ = b2-4ac
Δ = -2102-4·5·(-2)
Δ = 44140
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:

$\sqrt{\Delta}=\sqrt{44140}=\sqrt{4*11035}=\sqrt{4}*\sqrt{11035}=2\sqrt{11035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11035}}{2*5}=\frac{210-2\sqrt{11035}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11035}}{2*5}=\frac{210+2\sqrt{11035}}{10}
$