2/5x-53x=4

Solution for 2/5x-53x=4 equation:

2/5x-53x=4

We move all terms to the left:

2/5x-53x-(4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-53x+2/5x-4=0

We multiply all the terms by the denominator


-53x*5x-4*5x+2=0

Wy multiply elements

-265x^2-20x+2=0

a = -265; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·(-265)·2
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{70}}{2*-265}=\frac{20-6\sqrt{70}}{-530}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{70}}{2*-265}=\frac{20+6\sqrt{70}}{-530}
$