4x=2/5x-10

Solution for 4x=2/5x-10 equation:

4x=2/5x-10

We move all terms to the left:

4x-(2/5x-10)=0


Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

4x-2/5x+10=0

We multiply all the terms by the denominator


4x*5x+10*5x-2=0

Wy multiply elements

20x^2+50x-2=0

a = 20; b = 50; c = -2;
Δ = b2-4ac
Δ = 502-4·20·(-2)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{665}}{2*20}=\frac{-50-2\sqrt{665}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{665}}{2*20}=\frac{-50+2\sqrt{665}}{40}
$