2/5x=5x+3

Solution for 2/5x=5x+3 equation:

2/5x=5x+3

We move all terms to the left:

2/5x-(5x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-5x-3=0

We multiply all the terms by the denominator


-5x*5x-3*5x+2=0

Wy multiply elements

-25x^2-15x+2=0

a = -25; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-25)·2
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{17}}{2*-25}=\frac{15-5\sqrt{17}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{17}}{2*-25}=\frac{15+5\sqrt{17}}{-50}
$